-7p^2+8p+32=8

Solution for -7p^2+8p+32=8 equation:

-7p^2+8p+32=8

We move all terms to the left:

-7p^2+8p+32-(8)=0

We add all the numbers together, and all the variables

-7p^2+8p+24=0

a = -7; b = 8; c = +24;
Δ = b2-4ac
Δ = 82-4·(-7)·24
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{-(8)-4\sqrt{46}}{2*-7}=\frac{-8-4\sqrt{46}}{-14}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+4\sqrt{46}}{2*-7}=\frac{-8+4\sqrt{46}}{-14}
$