p/2p+3p+2+p=-4

Solution for p/2p+3p+2+p=-4 equation:

p/2p+3p+2+p=-4

We move all terms to the left:

p/2p+3p+2+p-(-4)=0


Domain of the equation: 2p!=0

p!=0/2

p!=0

p∈R


We add all the numbers together, and all the variables

4p+p/2p+6=0

We multiply all the terms by the denominator


4p*2p+p+6*2p=0

We add all the numbers together, and all the variables

p+4p*2p+6*2p=0

Wy multiply elements

8p^2+p+12p=0

We add all the numbers together, and all the variables

8p^2+13p=0

a = 8; b = 13; c = 0;
Δ = b2-4ac
Δ = 132-4·8·0
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-13}{2*8}=\frac{-26}{16}
=-1+5/8
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+13}{2*8}=\frac{0}{16}
=0
$