21x=x^2-18

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

21x=x^2-18

We move all terms to the left:

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

We get rid of parentheses

-x^2+21x+18=0

We add all the numbers together, and all the variables

-1x^2+21x+18=0

a = -1; b = 21; c = +18;
Δ = b2-4ac
Δ = 212-4·(-1)·18
Δ = 513
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:

$\sqrt{\Delta}=\sqrt{513}=\sqrt{9*57}=\sqrt{9}*\sqrt{57}=3\sqrt{57}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-3\sqrt{57}}{2*-1}=\frac{-21-3\sqrt{57}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+3\sqrt{57}}{2*-1}=\frac{-21+3\sqrt{57}}{-2}
$