(5x+4)(9x-8)=180

Solution for (5x+4)(9x-8)=180 equation:

(5x+4)(9x-8)=180

We move all terms to the left:

(5x+4)(9x-8)-(180)=0

We multiply parentheses ..

(+45x^2-40x+36x-32)-180=0

We get rid of parentheses

45x^2-40x+36x-32-180=0

We add all the numbers together, and all the variables

45x^2-4x-212=0

a = 45; b = -4; c = -212;
Δ = b2-4ac
Δ = -42-4·45·(-212)
Δ = 38176
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:

$\sqrt{\Delta}=\sqrt{38176}=\sqrt{16*2386}=\sqrt{16}*\sqrt{2386}=4\sqrt{2386}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{2386}}{2*45}=\frac{4-4\sqrt{2386}}{90}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{2386}}{2*45}=\frac{4+4\sqrt{2386}}{90}
$