# Solving Quadratic Equations: A Step-by-Step Guide to 4x^2 – 5x – 12 = 0

Are you struggling with quadratic equations and don’t know where to start? Look no further! Quadratic equations are “4x ^ 2 – 5x – 12 = 0″an essential part of mathematics that can be used in countless real-world applications. However, they can be difficult to solve without proper guidance. In this step-by-step guide, we will break down a specific example: “4x ^ 2 – 5x – 12 = 0”. dive into the world of quadratic equations together!

## What is a Quadratic Equation?

depending on their discriminant (b^2 – 4ac). A discriminant greater than zero indicates there are two distinct real solutions; when it’s equal to zero there’s only one real solution while if it’s less than zero then no real solutions exist.

Quadratic equations play an important role in many areas “4x ^ 2 – 5x – 12 = 0”. such as physics, engineering and finance just to mention few examples.

## Steps to Solve Quadratic Equations

Solving quadratic equations may seem daunting, but it’s actually a straightforward process that can be done by following a set of steps. 1: Identify the coefficients – In any quadratic “4x ^ 2 – 5x – 12 = 0”. equation, there will always be three coefficients – A, B and C. A represents the coefficient of x^2 term, B represents the coefficient of x term and C represents the constant.

By using these four simple steps you’ll be able to solve any quadratic equation quite easily!

## Example: 4x^2 – 5x – 12 = 0

Let’s put the steps we learned into practice with a specific example”4x ^ 2 – 5x – 12 = 0″.

Step 1 is to identify the values of a, b, and c in the equation. In this case, a = 4, b = -5, and c = -12.

Step 2 is to plug these values into the quadratic formula: x = (-b ± √(b^2-4ac)) / (2a).

### So for our example equation, we get:

x = (-(-5) ± √((-5)^2-4(4)(-12))) / (2(4))

### which simplifies to:

x = (5 ± √241) / 8

These are our two solutions for x. Note that because of the square root term inside them (√241), they are not rational numbers and cannot be simplified further.

We can check these solutions by plugging them make it true. It’s important to always do this step as it ensures that any extraneous solutions (solutions that work mathematically but don’t make sense in context) are eliminated.

Solving quadratic equations involves following specific “4x ^ 2 – 5x – 12 = 0” steps like identifying coefficients a,b,c; applying the quadratic formula; finding possible roots or solutions; checking those answers against given conditions. With practice you will become more comfortable working through quadratics!

## Conclusion

Quadratic equations can seem daunting at first, but with practice and the knowledge of the steps involved in solving them, they become much more manageable. Remembering to always use the quadratic formula or factoring method, depending on the equation, will make it easier for you to solve them efficiently.

The example we used in this post was “4x ^ 2 – 5x – 12 = 0”. By following the step-by-step guide provided above, we were able to find that x = -1.5 and x = 2 as solutions for this equation.

So next time you encounter a quadratic equation like this one or any other variation of it, don’t let it intimidate you! carefully until you arrive at a solution. With enough practice and persistence, solving quadratic equations will soon become second nature to you “4x ^ 2 – 5x – 12 = 0”.