53=8y^2

Solution for 53=8y^2 equation:

53=8y^2

We move all terms to the left:

53-(8y^2)=0

a = -8; b = 0; c = +53;
Δ = b2-4ac
Δ = 02-4·(-8)·53
Δ = 1696
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:

$\sqrt{\Delta}=\sqrt{1696}=\sqrt{16*106}=\sqrt{16}*\sqrt{106}=4\sqrt{106}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{106}}{2*-8}=\frac{0-4\sqrt{106}}{-16}
=-\frac{4\sqrt{106}}{-16}
=-\frac{\sqrt{106}}{-4}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{106}}{2*-8}=\frac{0+4\sqrt{106}}{-16}
=\frac{4\sqrt{106}}{-16}
=\frac{\sqrt{106}}{-4}
$