(x^2)=1250

Solution for (x^2)=1250 equation:

(x^2)=1250

We move all terms to the left:

(x^2)-(1250)=0

a = 1; b = 0; c = -1250;
Δ = b2-4ac
Δ = 02-4·1·(-1250)
Δ = 5000
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:

$\sqrt{\Delta}=\sqrt{5000}=\sqrt{2500*2}=\sqrt{2500}*\sqrt{2}=50\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-50\sqrt{2}}{2*1}=\frac{0-50\sqrt{2}}{2}
=-\frac{50\sqrt{2}}{2}
=-25\sqrt{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+50\sqrt{2}}{2*1}=\frac{0+50\sqrt{2}}{2}
=\frac{50\sqrt{2}}{2}
=25\sqrt{2}
$