(4x-20)(x)=180

Solution for (4x-20)(x)=180 equation:

(4x-20)(x)=180

We move all terms to the left:

(4x-20)(x)-(180)=0

We multiply parentheses

4x^2-20x-180=0

a = 4; b = -20; c = -180;
Δ = b2-4ac
Δ = -202-4·4·(-180)
Δ = 3280
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:

$\sqrt{\Delta}=\sqrt{3280}=\sqrt{16*205}=\sqrt{16}*\sqrt{205}=4\sqrt{205}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-4\sqrt{205}}{2*4}=\frac{20-4\sqrt{205}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+4\sqrt{205}}{2*4}=\frac{20+4\sqrt{205}}{8}
$