5x(x-12)=180

Solution for 5x(x-12)=180 equation:

5x(x-12)=180

We move all terms to the left:

5x(x-12)-(180)=0

We multiply parentheses

5x^2-60x-180=0

a = 5; b = -60; c = -180;
Δ = b2-4ac
Δ = -602-4·5·(-180)
Δ = 7200
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:

$\sqrt{\Delta}=\sqrt{7200}=\sqrt{3600*2}=\sqrt{3600}*\sqrt{2}=60\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-60\sqrt{2}}{2*5}=\frac{60-60\sqrt{2}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+60\sqrt{2}}{2*5}=\frac{60+60\sqrt{2}}{10}
$