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

Solution for 2p(p+2)-3p(2p-3)=0 equation:

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

We multiply parentheses

2p^2-6p^2+4p+9p=0

We add all the numbers together, and all the variables

-4p^2+13p=0

a = -4; b = 13; c = 0;
Δ = b2-4ac
Δ = 132-4·(-4)·0
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-13}{2*-4}=\frac{-26}{-8}
=3+1/4
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+13}{2*-4}=\frac{0}{-8}
=0
$