y2=500

Solution for y2=500 equation:

y2=500

We move all terms to the left:

y2-(500)=0

We add all the numbers together, and all the variables

y^2-500=0

a = 1; b = 0; c = -500;
Δ = b2-4ac
Δ = 02-4·1·(-500)
Δ = 2000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{2000}=\sqrt{400*5}=\sqrt{400}*\sqrt{5}=20\sqrt{5}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-20\sqrt{5}}{2*1}=\frac{0-20\sqrt{5}}{2}
=-\frac{20\sqrt{5}}{2}
=-10\sqrt{5}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+20\sqrt{5}}{2*1}=\frac{0+20\sqrt{5}}{2}
=\frac{20\sqrt{5}}{2}
=10\sqrt{5}
$