6x(x+12)=180

Solution for 6x(x+12)=180 equation:

6x(x+12)=180

We move all terms to the left:

6x(x+12)-(180)=0

We multiply parentheses

6x^2+72x-180=0

a = 6; b = 72; c = -180;
Δ = b2-4ac
Δ = 722-4·6·(-180)
Δ = 9504
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:

$\sqrt{\Delta}=\sqrt{9504}=\sqrt{144*66}=\sqrt{144}*\sqrt{66}=12\sqrt{66}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(72)-12\sqrt{66}}{2*6}=\frac{-72-12\sqrt{66}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(72)+12\sqrt{66}}{2*6}=\frac{-72+12\sqrt{66}}{12}
$