X^2=-x^2+18x

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

X^2=-X^2+18X

We move all terms to the left:

X^2-(-X^2+18X)=0

We get rid of parentheses

X^2+X^2-18X=0

We add all the numbers together, and all the variables

2X^2-18X=0

a = 2; b = -18; c = 0;
Δ = b2-4ac
Δ = -182-4·2·0
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-18}{2*2}=\frac{0}{4}
=0
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+18}{2*2}=\frac{36}{4}
=9
$