x^2=2x+21

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

x^2=2x+21

We move all terms to the left:

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

We get rid of parentheses

x^2-2x-21=0

a = 1; b = -2; c = -21;
Δ = b2-4ac
Δ = -22-4·1·(-21)
Δ = 88
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:

$\sqrt{\Delta}=\sqrt{88}=\sqrt{4*22}=\sqrt{4}*\sqrt{22}=2\sqrt{22}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{22}}{2*1}=\frac{2-2\sqrt{22}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{22}}{2*1}=\frac{2+2\sqrt{22}}{2}
$