2=2x^2+6x-7

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

2=2x^2+6x-7

We move all terms to the left:

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

We get rid of parentheses

-2x^2-6x+7+2=0

We add all the numbers together, and all the variables

-2x^2-6x+9=0

a = -2; b = -6; c = +9;
Δ = b2-4ac
Δ = -62-4·(-2)·9
Δ = 108
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:

$\sqrt{\Delta}=\sqrt{108}=\sqrt{36*3}=\sqrt{36}*\sqrt{3}=6\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6\sqrt{3}}{2*-2}=\frac{6-6\sqrt{3}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6\sqrt{3}}{2*-2}=\frac{6+6\sqrt{3}}{-4}
$