x^2-2+6x+2=2x^2-22

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

x^2-2+6x+2=2x^2-22

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

x^2-2x^2+6x+22=0

We add all the numbers together, and all the variables

-1x^2+6x+22=0

a = -1; b = 6; c = +22;
Δ = b2-4ac
Δ = 62-4·(-1)·22
Δ = 124
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:

$\sqrt{\Delta}=\sqrt{124}=\sqrt{4*31}=\sqrt{4}*\sqrt{31}=2\sqrt{31}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{31}}{2*-1}=\frac{-6-2\sqrt{31}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{31}}{2*-1}=\frac{-6+2\sqrt{31}}{-2}
$