(12+x)x=180

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

(12+x)x=180

We move all terms to the left:

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

We add all the numbers together, and all the variables

(x+12)x-180=0

We multiply parentheses

x^2+12x-180=0

a = 1; b = 12; c = -180;
Δ = b2-4ac
Δ = 122-4·1·(-180)
Δ = 864
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:

$\sqrt{\Delta}=\sqrt{864}=\sqrt{144*6}=\sqrt{144}*\sqrt{6}=12\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-12\sqrt{6}}{2*1}=\frac{-12-12\sqrt{6}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+12\sqrt{6}}{2*1}=\frac{-12+12\sqrt{6}}{2}
$