x^2+12x=66

Solution for x^2+12x=66 equation:

x^2+12x=66

We move all terms to the left:

x^2+12x-(66)=0

a = 1; b = 12; c = -66;
Δ = b2-4ac
Δ = 122-4·1·(-66)
Δ = 408
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:

$\sqrt{\Delta}=\sqrt{408}=\sqrt{4*102}=\sqrt{4}*\sqrt{102}=2\sqrt{102}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-2\sqrt{102}}{2*1}=\frac{-12-2\sqrt{102}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+2\sqrt{102}}{2*1}=\frac{-12+2\sqrt{102}}{2}
$