12x^2+36x=27=0

Solution for 12x^2+36x=27=0 equation:

12x^2+36x=27=0

We move all terms to the left:

12x^2+36x-(27)=0

a = 12; b = 36; c = -27;
Δ = b2-4ac
Δ = 362-4·12·(-27)
Δ = 2592
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:

$\sqrt{\Delta}=\sqrt{2592}=\sqrt{1296*2}=\sqrt{1296}*\sqrt{2}=36\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-36\sqrt{2}}{2*12}=\frac{-36-36\sqrt{2}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+36\sqrt{2}}{2*12}=\frac{-36+36\sqrt{2}}{24}
$