0=y^2-50

Solution for 0=y^2-50 equation:

0=y^2-50

We move all terms to the left:

0-(y^2-50)=0

We add all the numbers together, and all the variables

-(y^2-50)=0

We get rid of parentheses

-y^2+50=0

We add all the numbers together, and all the variables

-1y^2+50=0

a = -1; b = 0; c = +50;
Δ = b2-4ac
Δ = 02-4·(-1)·50
Δ = 200
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:

$\sqrt{\Delta}=\sqrt{200}=\sqrt{100*2}=\sqrt{100}*\sqrt{2}=10\sqrt{2}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{2}}{2*-1}=\frac{0-10\sqrt{2}}{-2}
=-\frac{10\sqrt{2}}{-2}
=-\frac{5\sqrt{2}}{-1}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{2}}{2*-1}=\frac{0+10\sqrt{2}}{-2}
=\frac{10\sqrt{2}}{-2}
=\frac{5\sqrt{2}}{-1}
$