64y2-10=9

Solution for 64y2-10=9 equation:

64y^2-10=9

We move all terms to the left:

64y^2-10-(9)=0

We add all the numbers together, and all the variables

64y^2-19=0

a = 64; b = 0; c = -19;
Δ = b2-4ac
Δ = 02-4·64·(-19)
Δ = 4864
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:

$\sqrt{\Delta}=\sqrt{4864}=\sqrt{256*19}=\sqrt{256}*\sqrt{19}=16\sqrt{19}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-16\sqrt{19}}{2*64}=\frac{0-16\sqrt{19}}{128}
=-\frac{16\sqrt{19}}{128}
=-\frac{\sqrt{19}}{8}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+16\sqrt{19}}{2*64}=\frac{0+16\sqrt{19}}{128}
=\frac{16\sqrt{19}}{128}
=\frac{\sqrt{19}}{8}
$