-8-8p2=-31

Solution for -8-8p2=-31 equation:

-8-8p^2=-31

We move all terms to the left:

-8-8p^2-(-31)=0

We add all the numbers together, and all the variables

-8p^2+23=0

a = -8; b = 0; c = +23;
Δ = b2-4ac
Δ = 02-4·(-8)·23
Δ = 736
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:

$\sqrt{\Delta}=\sqrt{736}=\sqrt{16*46}=\sqrt{16}*\sqrt{46}=4\sqrt{46}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{46}}{2*-8}=\frac{0-4\sqrt{46}}{-16}
=-\frac{4\sqrt{46}}{-16}
=-\frac{\sqrt{46}}{-4}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{46}}{2*-8}=\frac{0+4\sqrt{46}}{-16}
=\frac{4\sqrt{46}}{-16}
=\frac{\sqrt{46}}{-4}
$