25y^2=50

Solution for 25y^2=50 equation:

25y^2=50

We move all terms to the left:

25y^2-(50)=0

a = 25; b = 0; c = -50;
Δ = b2-4ac
Δ = 02-4·25·(-50)
Δ = 5000
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:

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