6x^2-6=7

Solution for 6x^2-6=7 equation:

6x^2-6=7

We move all terms to the left:

6x^2-6-(7)=0

We add all the numbers together, and all the variables

6x^2-13=0

a = 6; b = 0; c = -13;
Δ = b2-4ac
Δ = 02-4·6·(-13)
Δ = 312
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:

$\sqrt{\Delta}=\sqrt{312}=\sqrt{4*78}=\sqrt{4}*\sqrt{78}=2\sqrt{78}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{78}}{2*6}=\frac{0-2\sqrt{78}}{12}
=-\frac{2\sqrt{78}}{12}
=-\frac{\sqrt{78}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{78}}{2*6}=\frac{0+2\sqrt{78}}{12}
=\frac{2\sqrt{78}}{12}
=\frac{\sqrt{78}}{6}
$