y^2/5=121

Solution for y^2/5=121 equation:

y^2/5=121

We move all terms to the left:

y^2/5-(121)=0

We multiply all the terms by the denominator


y^2-121*5=0

We add all the numbers together, and all the variables

y^2-605=0

a = 1; b = 0; c = -605;
Δ = b2-4ac
Δ = 02-4·1·(-605)
Δ = 2420
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:

$\sqrt{\Delta}=\sqrt{2420}=\sqrt{484*5}=\sqrt{484}*\sqrt{5}=22\sqrt{5}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-22\sqrt{5}}{2*1}=\frac{0-22\sqrt{5}}{2}
=-\frac{22\sqrt{5}}{2}
=-11\sqrt{5}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+22\sqrt{5}}{2*1}=\frac{0+22\sqrt{5}}{2}
=\frac{22\sqrt{5}}{2}
=11\sqrt{5}
$