5p(2p+4)=10

Solution for 5p(2p+4)=10 equation:

5p(2p+4)=10

We move all terms to the left:

5p(2p+4)-(10)=0

We multiply parentheses

10p^2+20p-10=0

a = 10; b = 20; c = -10;
Δ = b2-4ac
Δ = 202-4·10·(-10)
Δ = 800
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:

$\sqrt{\Delta}=\sqrt{800}=\sqrt{400*2}=\sqrt{400}*\sqrt{2}=20\sqrt{2}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-20\sqrt{2}}{2*10}=\frac{-20-20\sqrt{2}}{20}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+20\sqrt{2}}{2*10}=\frac{-20+20\sqrt{2}}{20}
$