x^2=2x^2-22x+85

Solution for x^2=2x^2-22x+85 equation:

x^2=2x^2-22x+85

We move all terms to the left:

x^2-(2x^2-22x+85)=0

We get rid of parentheses

x^2-2x^2+22x-85=0

We add all the numbers together, and all the variables

-1x^2+22x-85=0

a = -1; b = 22; c = -85;
Δ = b2-4ac
Δ = 222-4·(-1)·(-85)
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-12}{2*-1}=\frac{-34}{-2}
=+17
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+12}{2*-1}=\frac{-10}{-2}
=+5
$