64p^2-10=11

Solution for 64p^2-10=11 equation:

64p^2-10=11

We move all terms to the left:

64p^2-10-(11)=0

We add all the numbers together, and all the variables

64p^2-21=0

a = 64; b = 0; c = -21;
Δ = b2-4ac
Δ = 02-4·64·(-21)
Δ = 5376
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{5376}=\sqrt{256*21}=\sqrt{256}*\sqrt{21}=16\sqrt{21}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-16\sqrt{21}}{2*64}=\frac{0-16\sqrt{21}}{128}
=-\frac{16\sqrt{21}}{128}
=-\frac{\sqrt{21}}{8}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+16\sqrt{21}}{2*64}=\frac{0+16\sqrt{21}}{128}
=\frac{16\sqrt{21}}{128}
=\frac{\sqrt{21}}{8}
$