(2x-9)(2x+4)=180

Solution for (2x-9)(2x+4)=180 equation:

(2x-9)(2x+4)=180

We move all terms to the left:

(2x-9)(2x+4)-(180)=0

We multiply parentheses ..

(+4x^2+8x-18x-36)-180=0

We get rid of parentheses

4x^2+8x-18x-36-180=0

We add all the numbers together, and all the variables

4x^2-10x-216=0

a = 4; b = -10; c = -216;
Δ = b2-4ac
Δ = -102-4·4·(-216)
Δ = 3556
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{3556}=\sqrt{4*889}=\sqrt{4}*\sqrt{889}=2\sqrt{889}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{889}}{2*4}=\frac{10-2\sqrt{889}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{889}}{2*4}=\frac{10+2\sqrt{889}}{8}
$