2(3p+5)p=13-2p+15

Solution for 2(3p+5)p=13-2p+15 equation:

2(3p+5)p=13-2p+15

We move all terms to the left:

2(3p+5)p-(13-2p+15)=0

We add all the numbers together, and all the variables

2(3p+5)p-(-2p+28)=0

We multiply parentheses

6p^2+10p-(-2p+28)=0

We get rid of parentheses

6p^2+10p+2p-28=0

We add all the numbers together, and all the variables

6p^2+12p-28=0

a = 6; b = 12; c = -28;
Δ = b2-4ac
Δ = 122-4·6·(-28)
Δ = 816
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:

$\sqrt{\Delta}=\sqrt{816}=\sqrt{16*51}=\sqrt{16}*\sqrt{51}=4\sqrt{51}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-4\sqrt{51}}{2*6}=\frac{-12-4\sqrt{51}}{12}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+4\sqrt{51}}{2*6}=\frac{-12+4\sqrt{51}}{12}
$