22.5=x^2

Solution for 22.5=x^2 equation:

22.5=x^2

We move all terms to the left:

22.5-(x^2)=0

We add all the numbers together, and all the variables

-1x^2+22.5=0

a = -1; b = 0; c = +22.5;
Δ = b2-4ac
Δ = 02-4·(-1)·22.5
Δ = 90
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:

$\sqrt{\Delta}=\sqrt{90}=\sqrt{9*10}=\sqrt{9}*\sqrt{10}=3\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-3\sqrt{10}}{2*-1}=\frac{0-3\sqrt{10}}{-2}
=-\frac{3\sqrt{10}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+3\sqrt{10}}{2*-1}=\frac{0+3\sqrt{10}}{-2}
=\frac{3\sqrt{10}}{-2}
$