2y^2=19

Solution for 2y^2=19 equation:

2y^2=19

We move all terms to the left:

2y^2-(19)=0

a = 2; b = 0; c = -19;
Δ = b2-4ac
Δ = 02-4·2·(-19)
Δ = 152
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:

$\sqrt{\Delta}=\sqrt{152}=\sqrt{4*38}=\sqrt{4}*\sqrt{38}=2\sqrt{38}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{38}}{2*2}=\frac{0-2\sqrt{38}}{4}
=-\frac{2\sqrt{38}}{4}
=-\frac{\sqrt{38}}{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{38}}{2*2}=\frac{0+2\sqrt{38}}{4}
=\frac{2\sqrt{38}}{4}
=\frac{\sqrt{38}}{2}
$