6x^2-6=162

Solution for 6x^2-6=162 equation:

6x^2-6=162

We move all terms to the left:

6x^2-6-(162)=0

We add all the numbers together, and all the variables

6x^2-168=0

a = 6; b = 0; c = -168;
Δ = b2-4ac
Δ = 02-4·6·(-168)
Δ = 4032
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:

$\sqrt{\Delta}=\sqrt{4032}=\sqrt{576*7}=\sqrt{576}*\sqrt{7}=24\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-24\sqrt{7}}{2*6}=\frac{0-24\sqrt{7}}{12}
=-\frac{24\sqrt{7}}{12}
=-2\sqrt{7}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+24\sqrt{7}}{2*6}=\frac{0+24\sqrt{7}}{12}
=\frac{24\sqrt{7}}{12}
=2\sqrt{7}
$