4x(x-6)=180

Solution for 4x(x-6)=180 equation:

4x(x-6)=180

We move all terms to the left:

4x(x-6)-(180)=0

We multiply parentheses

4x^2-24x-180=0

a = 4; b = -24; c = -180;
Δ = b2-4ac
Δ = -242-4·4·(-180)
Δ = 3456
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:

$\sqrt{\Delta}=\sqrt{3456}=\sqrt{576*6}=\sqrt{576}*\sqrt{6}=24\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-24\sqrt{6}}{2*4}=\frac{24-24\sqrt{6}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+24\sqrt{6}}{2*4}=\frac{24+24\sqrt{6}}{8}
$