2p^2-24=-16p

Solution for 2p^2-24=-16p equation:

2p^2-24=-16p

We move all terms to the left:

2p^2-24-(-16p)=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 = 448
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:

$\sqrt{\Delta}=\sqrt{448}=\sqrt{64*7}=\sqrt{64}*\sqrt{7}=8\sqrt{7}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-8\sqrt{7}}{2*2}=\frac{-16-8\sqrt{7}}{4}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+8\sqrt{7}}{2*2}=\frac{-16+8\sqrt{7}}{4}
$