5y^2-3=118

Solution for 5y^2-3=118 equation:

5y^2-3=118

We move all terms to the left:

5y^2-3-(118)=0

We add all the numbers together, and all the variables

5y^2-121=0

a = 5; b = 0; c = -121;
Δ = b2-4ac
Δ = 02-4·5·(-121)
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*5}=\frac{0-22\sqrt{5}}{10}
=-\frac{22\sqrt{5}}{10}
=-\frac{11\sqrt{5}}{5}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+22\sqrt{5}}{2*5}=\frac{0+22\sqrt{5}}{10}
=\frac{22\sqrt{5}}{10}
=\frac{11\sqrt{5}}{5}
$