8p^2-p-31=-11

Solution for 8p^2-p-31=-11 equation:

8p^2-p-31=-11

We move all terms to the left:

8p^2-p-31-(-11)=0

We add all the numbers together, and all the variables

8p^2-1p-20=0

a = 8; b = -1; c = -20;
Δ = b2-4ac
Δ = -12-4·8·(-20)
Δ = 641
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-\sqrt{641}}{2*8}=\frac{1-\sqrt{641}}{16}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{641}}{2*8}=\frac{1+\sqrt{641}}{16}
$