8p^2=24+16p

Solution for 8p^2=24+16p equation:

8p^2=24+16p

We move all terms to the left:

8p^2-(24+16p)=0

We add all the numbers together, and all the variables

8p^2-(16p+24)=0

We get rid of parentheses

8p^2-16p-24=0

a = 8; b = -16; c = -24;
Δ = b2-4ac
Δ = -162-4·8·(-24)
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-32}{2*8}=\frac{-16}{16}
=-1
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+32}{2*8}=\frac{48}{16}
=3
$