x^2=-21+18x

Solution for x^2=-21+18x equation:

x^2=-21+18x

We move all terms to the left:

x^2-(-21+18x)=0

We add all the numbers together, and all the variables

x^2-(18x-21)=0

We get rid of parentheses

x^2-18x+21=0

a = 1; b = -18; c = +21;
Δ = b2-4ac
Δ = -182-4·1·21
Δ = 240
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:

$\sqrt{\Delta}=\sqrt{240}=\sqrt{16*15}=\sqrt{16}*\sqrt{15}=4\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-4\sqrt{15}}{2*1}=\frac{18-4\sqrt{15}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+4\sqrt{15}}{2*1}=\frac{18+4\sqrt{15}}{2}
$