78=2y^2

Solution for 78=2y^2 equation:

78=2y^2

We move all terms to the left:

78-(2y^2)=0

a = -2; b = 0; c = +78;
Δ = b2-4ac
Δ = 02-4·(-2)·78
Δ = 624
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:

$\sqrt{\Delta}=\sqrt{624}=\sqrt{16*39}=\sqrt{16}*\sqrt{39}=4\sqrt{39}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{39}}{2*-2}=\frac{0-4\sqrt{39}}{-4}
=-\frac{4\sqrt{39}}{-4}
=-\frac{\sqrt{39}}{-1}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{39}}{2*-2}=\frac{0+4\sqrt{39}}{-4}
=\frac{4\sqrt{39}}{-4}
=\frac{\sqrt{39}}{-1}
$