X^2+36x=-12

Solution for X^2+36x=-12 equation:

X^2+36X=-12

We move all terms to the left:

X^2+36X-(-12)=0

We add all the numbers together, and all the variables

X^2+36X+12=0

a = 1; b = 36; c = +12;
Δ = b2-4ac
Δ = 362-4·1·12
Δ = 1248
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:

$\sqrt{\Delta}=\sqrt{1248}=\sqrt{16*78}=\sqrt{16}*\sqrt{78}=4\sqrt{78}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-4\sqrt{78}}{2*1}=\frac{-36-4\sqrt{78}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+4\sqrt{78}}{2*1}=\frac{-36+4\sqrt{78}}{2}
$