6x^2-12=33

Solution for 6x^2-12=33 equation:

6x^2-12=33

We move all terms to the left:

6x^2-12-(33)=0

We add all the numbers together, and all the variables

6x^2-45=0

a = 6; b = 0; c = -45;
Δ = b2-4ac
Δ = 02-4·6·(-45)
Δ = 1080
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:

$\sqrt{\Delta}=\sqrt{1080}=\sqrt{36*30}=\sqrt{36}*\sqrt{30}=6\sqrt{30}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{30}}{2*6}=\frac{0-6\sqrt{30}}{12}
=-\frac{6\sqrt{30}}{12}
=-\frac{\sqrt{30}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{30}}{2*6}=\frac{0+6\sqrt{30}}{12}
=\frac{6\sqrt{30}}{12}
=\frac{\sqrt{30}}{2}
$