(5x-32)(x-8)=180

Solution for (5x-32)(x-8)=180 equation:

(5x-32)(x-8)=180

We move all terms to the left:

(5x-32)(x-8)-(180)=0

We multiply parentheses ..

(+5x^2-40x-32x+256)-180=0

We get rid of parentheses

5x^2-40x-32x+256-180=0

We add all the numbers together, and all the variables

5x^2-72x+76=0

a = 5; b = -72; c = +76;
Δ = b2-4ac
Δ = -722-4·5·76
Δ = 3664
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:

$\sqrt{\Delta}=\sqrt{3664}=\sqrt{16*229}=\sqrt{16}*\sqrt{229}=4\sqrt{229}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-72)-4\sqrt{229}}{2*5}=\frac{72-4\sqrt{229}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-72)+4\sqrt{229}}{2*5}=\frac{72+4\sqrt{229}}{10}
$