p(3p+1)+(5p*p)=0

Solution for p(3p+1)+(5p*p)=0 equation:

p(3p+1)+(5p*p)=0

We add all the numbers together, and all the variables

p(3p+1)+(+5p*p)=0

We multiply parentheses

3p^2+p+(+5p*p)=0

We get rid of parentheses

3p^2+p+5p*p=0

Wy multiply elements

3p^2+5p^2+p=0

We add all the numbers together, and all the variables

8p^2+p=0

a = 8; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·8·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-1}{2*8}=\frac{-2}{16}
=-1/8
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*8}=\frac{0}{16}
=0
$