2p^2-3p=20-p^2

Solution for 2p^2-3p=20-p^2 equation:

2p^2-3p=20-p^2

We move all terms to the left:

2p^2-3p-(20-p^2)=0

We get rid of parentheses

2p^2+p^2-3p-20=0

We add all the numbers together, and all the variables

3p^2-3p-20=0

a = 3; b = -3; c = -20;
Δ = b2-4ac
Δ = -32-4·3·(-20)
Δ = 249
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-\sqrt{249}}{2*3}=\frac{3-\sqrt{249}}{6}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{249}}{2*3}=\frac{3+\sqrt{249}}{6}
$