# 4x^2-5x-12=0: Easy Step by Step Solution

Are you struggling to find the solutions to 4x^2-5x-12=0? Look no further! In this solution, we’ll guide you step-by-step through the process of solving the quadratic equation 4x^2 – 5x – 12 = 0 using the quadratic formula. Get ready to discover the exact solutions to this equation and impress your math teacher with your newfound skills!

To solve the quadratic equation 4x^2 – 5x – 12 = 0, you can use the quadratic formula:

x = (-b ± √(b^2 – 4ac)) / 2a

where a = 4, b = -5, and c = -12.

Substituting these values into the formula, we get:

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

Simplifying this expression:

x = (5 ± √(25 + 192)) / 8

x = (5 ± √217) / 8

So the solutions to the equation are:

x = (5 + √217) / 8

or

x = (5 – √217) / 8

These are the exact solutions to the equation. If you need decimal approximations, you can use a calculator to evaluate the square root of 217 and simplify the fractions.

## Explanation – 4x^2-5x-12=0

Here’s a step-by-step explanation of how to solve the quadratic equation 4x^2 – 5x – 12 = 0 using the quadratic formula:

Step 1: Identify the values of a, b, and c in the quadratic equation.

In the equation 4x^2 – 5x – 12 = 0, the coefficient of x^2 is 4, the coefficient of x is -5, and the constant term is -12. So, we have:

a = 4 b = -5 c = -12

Step 2: Substitute the values of a, b, and c into the quadratic formula.

x = (-b ± √(b^2 – 4ac)) / 2a

Substituting the values of a, b, and c, we get:

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

Step 3: Simplify the expression under the square root sign.

Simplifying the expression under the square root sign, we get:

√((-5)^2 – 4(4)(-12)) = √(25 + 192) = √217

Step 4: Simplify the expression inside the parentheses.

Simplifying the expression inside the parentheses, we get:

x = (5 ± √217) / 8

These are the exact solutions to the quadratic equation 4x^2 – 5x – 12 = 0. If you need decimal approximations, you can use a calculator to evaluate the square root of 217 and simplify the fractions.

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