x^2-18=18-x^2

Solution for x^2-18=18-x^2 equation:

x^2-18=18-x^2

We move all terms to the left:

x^2-18-(18-x^2)=0

We get rid of parentheses

x^2+x^2-18-18=0

We add all the numbers together, and all the variables

2x^2-36=0

a = 2; b = 0; c = -36;
Δ = b2-4ac
Δ = 02-4·2·(-36)
Δ = 288
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:

$\sqrt{\Delta}=\sqrt{288}=\sqrt{144*2}=\sqrt{144}*\sqrt{2}=12\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{2}}{2*2}=\frac{0-12\sqrt{2}}{4}
=-\frac{12\sqrt{2}}{4}
=-3\sqrt{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{2}}{2*2}=\frac{0+12\sqrt{2}}{4}
=\frac{12\sqrt{2}}{4}
=3\sqrt{2}
$