-6x^2+2x+23=2x^2+6

Solution for -6x^2+2x+23=2x^2+6 equation:

-6x^2+2x+23=2x^2+6

We move all terms to the left:

-6x^2+2x+23-(2x^2+6)=0

We get rid of parentheses

-6x^2-2x^2+2x-6+23=0

We add all the numbers together, and all the variables

-8x^2+2x+17=0

a = -8; b = 2; c = +17;
Δ = b2-4ac
Δ = 22-4·(-8)·17
Δ = 548
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:

$\sqrt{\Delta}=\sqrt{548}=\sqrt{4*137}=\sqrt{4}*\sqrt{137}=2\sqrt{137}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{137}}{2*-8}=\frac{-2-2\sqrt{137}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{137}}{2*-8}=\frac{-2+2\sqrt{137}}{-16}
$