-2p2=16p+24

Solution for -2p2=16p+24 equation:

-2p^2=16p+24

We move all terms to the left:

-2p^2-(16p+24)=0

We get rid of parentheses

-2p^2-16p-24=0

a = -2; b = -16; c = -24;
Δ = b2-4ac
Δ = -162-4·(-2)·(-24)
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-8}{2*-2}=\frac{8}{-4}
=-2
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+8}{2*-2}=\frac{24}{-4}
=-6
$