6x^2-27=12x

Solution for 6x^2-27=12x equation:

6x^2-27=12x

We move all terms to the left:

6x^2-27-(12x)=0

a = 6; b = -12; c = -27;
Δ = b2-4ac
Δ = -122-4·6·(-27)
Δ = 792
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:

$\sqrt{\Delta}=\sqrt{792}=\sqrt{36*22}=\sqrt{36}*\sqrt{22}=6\sqrt{22}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-6\sqrt{22}}{2*6}=\frac{12-6\sqrt{22}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+6\sqrt{22}}{2*6}=\frac{12+6\sqrt{22}}{12}
$