x^2=81.25

Solution for x^2=81.25 equation:

x^2=81.25

We move all terms to the left:

x^2-(81.25)=0

We add all the numbers together, and all the variables

x^2-81.25=0

a = 1; b = 0; c = -81.25;
Δ = b2-4ac
Δ = 02-4·1·(-81.25)
Δ = 325
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:

$\sqrt{\Delta}=\sqrt{325}=\sqrt{25*13}=\sqrt{25}*\sqrt{13}=5\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-5\sqrt{13}}{2*1}=\frac{0-5\sqrt{13}}{2}
=-\frac{5\sqrt{13}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+5\sqrt{13}}{2*1}=\frac{0+5\sqrt{13}}{2}
=\frac{5\sqrt{13}}{2}
$