2p(3p-5)=0

Solution for 2p(3p-5)=0 equation:

2p(3p-5)=0

We multiply parentheses

6p^2-10p=0

a = 6; b = -10; c = 0;
Δ = b2-4ac
Δ = -102-4·6·0
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-10}{2*6}=\frac{0}{12}
=0
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+10}{2*6}=\frac{20}{12}
=1+2/3
$