3p2=85-2p

Solution for 3p2=85-2p equation:

3p^2=85-2p

We move all terms to the left:

3p^2-(85-2p)=0

We add all the numbers together, and all the variables

3p^2-(-2p+85)=0

We get rid of parentheses

3p^2+2p-85=0

a = 3; b = 2; c = -85;
Δ = b2-4ac
Δ = 22-4·3·(-85)
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{-(2)-32}{2*3}=\frac{-34}{6}
=-5+2/3
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+32}{2*3}=\frac{30}{6}
=5
$