6x^2-22=33

Solution for 6x^2-22=33 equation:

6x^2-22=33

We move all terms to the left:

6x^2-22-(33)=0

We add all the numbers together, and all the variables

6x^2-55=0

a = 6; b = 0; c = -55;
Δ = b2-4ac
Δ = 02-4·6·(-55)
Δ = 1320
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:

$\sqrt{\Delta}=\sqrt{1320}=\sqrt{4*330}=\sqrt{4}*\sqrt{330}=2\sqrt{330}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{330}}{2*6}=\frac{0-2\sqrt{330}}{12}
=-\frac{2\sqrt{330}}{12}
=-\frac{\sqrt{330}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{330}}{2*6}=\frac{0+2\sqrt{330}}{12}
=\frac{2\sqrt{330}}{12}
=\frac{\sqrt{330}}{6}
$