5y^2-3=78

Solution for 5y^2-3=78 equation:

5y^2-3=78

We move all terms to the left:

5y^2-3-(78)=0

We add all the numbers together, and all the variables

5y^2-81=0

a = 5; b = 0; c = -81;
Δ = b2-4ac
Δ = 02-4·5·(-81)
Δ = 1620
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:

$\sqrt{\Delta}=\sqrt{1620}=\sqrt{324*5}=\sqrt{324}*\sqrt{5}=18\sqrt{5}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-18\sqrt{5}}{2*5}=\frac{0-18\sqrt{5}}{10}
=-\frac{18\sqrt{5}}{10}
=-\frac{9\sqrt{5}}{5}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+18\sqrt{5}}{2*5}=\frac{0+18\sqrt{5}}{10}
=\frac{18\sqrt{5}}{10}
=\frac{9\sqrt{5}}{5}
$