x^2=24.5

Solution for x^2=24.5 equation:

x^2=24.5

We move all terms to the left:

x^2-(24.5)=0

We add all the numbers together, and all the variables

x^2-24.5=0

a = 1; b = 0; c = -24.5;
Δ = b2-4ac
Δ = 02-4·1·(-24.5)
Δ = 98
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:

$\sqrt{\Delta}=\sqrt{98}=\sqrt{49*2}=\sqrt{49}*\sqrt{2}=7\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-7\sqrt{2}}{2*1}=\frac{0-7\sqrt{2}}{2}
=-\frac{7\sqrt{2}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+7\sqrt{2}}{2*1}=\frac{0+7\sqrt{2}}{2}
=\frac{7\sqrt{2}}{2}
$