5y2+19=64

Solution for 5y2+19=64 equation:

5y^2+19=64

We move all terms to the left:

5y^2+19-(64)=0

We add all the numbers together, and all the variables

5y^2-45=0

a = 5; b = 0; c = -45;
Δ = b2-4ac
Δ = 02-4·5·(-45)
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-30}{2*5}=\frac{-30}{10}
=-3
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+30}{2*5}=\frac{30}{10}
=3
$