x^2-12x=-17-x^2

Solution for x^2-12x=-17-x^2 equation:

x^2-12x=-17-x^2

We move all terms to the left:

x^2-12x-(-17-x^2)=0

We get rid of parentheses

x^2+x^2-12x+17=0

We add all the numbers together, and all the variables

2x^2-12x+17=0

a = 2; b = -12; c = +17;
Δ = b2-4ac
Δ = -122-4·2·17
Δ = 8
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:

$\sqrt{\Delta}=\sqrt{8}=\sqrt{4*2}=\sqrt{4}*\sqrt{2}=2\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{2}}{2*2}=\frac{12-2\sqrt{2}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{2}}{2*2}=\frac{12+2\sqrt{2}}{4}
$