3p^2-4p+p^2+9p=0

Solution for 3p^2-4p+p^2+9p=0 equation:

3p^2-4p+p^2+9p=0

We add all the numbers together, and all the variables

4p^2+5p=0

a = 4; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·4·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5}{2*4}=\frac{-10}{8}
=-1+1/4
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*4}=\frac{0}{8}
=0
$