27=3x^2+12x

Solution for 27=3x^2+12x equation:

27=3x^2+12x

We move all terms to the left:

27-(3x^2+12x)=0

We get rid of parentheses

-3x^2-12x+27=0

a = -3; b = -12; c = +27;
Δ = b2-4ac
Δ = -122-4·(-3)·27
Δ = 468
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:

$\sqrt{\Delta}=\sqrt{468}=\sqrt{36*13}=\sqrt{36}*\sqrt{13}=6\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-6\sqrt{13}}{2*-3}=\frac{12-6\sqrt{13}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+6\sqrt{13}}{2*-3}=\frac{12+6\sqrt{13}}{-6}
$