(x-5)(2x+3)=84

2 min read Jun 17, 2024

Solving the Quadratic Equation: (x-5)(2x+3) = 84

This article will guide you through solving the quadratic equation (x-5)(2x+3) = 84. We will use the following steps:

1. Expand the Equation

First, we need to expand the left side of the equation by multiplying the binomials:

(x-5)(2x+3) = 84
2x² + 3x - 10x - 15 = 84

Simplifying the equation:

2x² - 7x - 15 = 84

2. Move the Constant Term to the Left Side

To set the equation equal to zero, we need to move the constant term (84) to the left side:

2x² - 7x - 15 - 84 = 0
2x² - 7x - 99 = 0

3. Solve for x using the Quadratic Formula

Now that we have a standard quadratic equation in the form ax² + bx + c = 0, we can use the quadratic formula to find the values of x:

x = (-b ± √(b² - 4ac)) / 2a

In this case, a = 2, b = -7, and c = -99. Substituting these values into the formula:

x = (7 ± √((-7)² - 4 * 2 * -99)) / (2 * 2)
x = (7 ± √(49 + 792)) / 4
x = (7 ± √841) / 4
x = (7 ± 29) / 4

4. Find the Two Solutions

This gives us two possible solutions:

Conclusion

Therefore, the solutions to the quadratic equation (x-5)(2x+3) = 84 are x = 9 and x = -5.5.