2p(3p-5)=40

Solution for 2p(3p-5)=40 equation:

2p(3p-5)=40

We move all terms to the left:

2p(3p-5)-(40)=0

We multiply parentheses

6p^2-10p-40=0

a = 6; b = -10; c = -40;
Δ = b2-4ac
Δ = -102-4·6·(-40)
Δ = 1060
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1060}=\sqrt{4*265}=\sqrt{4}*\sqrt{265}=2\sqrt{265}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{265}}{2*6}=\frac{10-2\sqrt{265}}{12}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{265}}{2*6}=\frac{10+2\sqrt{265}}{12}
$