x(x+6)=132

Solution for x(x+6)=132 equation:

x(x+6)=132

We move all terms to the left:

x(x+6)-(132)=0

We multiply parentheses

x^2+6x-132=0

a = 1; b = 6; c = -132;
Δ = b2-4ac
Δ = 62-4·1·(-132)
Δ = 564
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:

$\sqrt{\Delta}=\sqrt{564}=\sqrt{4*141}=\sqrt{4}*\sqrt{141}=2\sqrt{141}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{141}}{2*1}=\frac{-6-2\sqrt{141}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{141}}{2*1}=\frac{-6+2\sqrt{141}}{2}
$