64y^2=24

Solution for 64y^2=24 equation:

64y^2=24

We move all terms to the left:

64y^2-(24)=0

a = 64; b = 0; c = -24;
Δ = b2-4ac
Δ = 02-4·64·(-24)
Δ = 6144
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:

$\sqrt{\Delta}=\sqrt{6144}=\sqrt{1024*6}=\sqrt{1024}*\sqrt{6}=32\sqrt{6}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-32\sqrt{6}}{2*64}=\frac{0-32\sqrt{6}}{128}
=-\frac{32\sqrt{6}}{128}
=-\frac{\sqrt{6}}{4}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+32\sqrt{6}}{2*64}=\frac{0+32\sqrt{6}}{128}
=\frac{32\sqrt{6}}{128}
=\frac{\sqrt{6}}{4}
$