7x(x-12)=180

Solution for 7x(x-12)=180 equation:

7x(x-12)=180

We move all terms to the left:

7x(x-12)-(180)=0

We multiply parentheses

7x^2-84x-180=0

a = 7; b = -84; c = -180;
Δ = b2-4ac
Δ = -842-4·7·(-180)
Δ = 12096
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:

$\sqrt{\Delta}=\sqrt{12096}=\sqrt{576*21}=\sqrt{576}*\sqrt{21}=24\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-84)-24\sqrt{21}}{2*7}=\frac{84-24\sqrt{21}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-84)+24\sqrt{21}}{2*7}=\frac{84+24\sqrt{21}}{14}
$