y^2/5=36

Solution for y^2/5=36 equation:

y^2/5=36

We move all terms to the left:

y^2/5-(36)=0

We multiply all the terms by the denominator


y^2-36*5=0

We add all the numbers together, and all the variables

y^2-180=0

a = 1; b = 0; c = -180;
Δ = b2-4ac
Δ = 02-4·1·(-180)
Δ = 720
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:

$\sqrt{\Delta}=\sqrt{720}=\sqrt{144*5}=\sqrt{144}*\sqrt{5}=12\sqrt{5}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{5}}{2*1}=\frac{0-12\sqrt{5}}{2}
=-\frac{12\sqrt{5}}{2}
=-6\sqrt{5}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{5}}{2*1}=\frac{0+12\sqrt{5}}{2}
=\frac{12\sqrt{5}}{2}
=6\sqrt{5}
$