6=2x^2-7

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

6=2x^2-7

We move all terms to the left:

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

We get rid of parentheses

-2x^2+7+6=0

We add all the numbers together, and all the variables

-2x^2+13=0

a = -2; b = 0; c = +13;
Δ = b2-4ac
Δ = 02-4·(-2)·13
Δ = 104
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:

$\sqrt{\Delta}=\sqrt{104}=\sqrt{4*26}=\sqrt{4}*\sqrt{26}=2\sqrt{26}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{26}}{2*-2}=\frac{0-2\sqrt{26}}{-4}
=-\frac{2\sqrt{26}}{-4}
=-\frac{\sqrt{26}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{26}}{2*-2}=\frac{0+2\sqrt{26}}{-4}
=\frac{2\sqrt{26}}{-4}
=\frac{\sqrt{26}}{-2}
$