p/5p+5+3p=21

Solution for p/5p+5+3p=21 equation:

p/5p+5+3p=21

We move all terms to the left:

p/5p+5+3p-(21)=0


Domain of the equation: 5p!=0

p!=0/5

p!=0

p∈R


We add all the numbers together, and all the variables

3p+p/5p-16=0

We multiply all the terms by the denominator


3p*5p+p-16*5p=0

We add all the numbers together, and all the variables

p+3p*5p-16*5p=0

Wy multiply elements

15p^2+p-80p=0

We add all the numbers together, and all the variables

15p^2-79p=0

a = 15; b = -79; c = 0;
Δ = b2-4ac
Δ = -792-4·15·0
Δ = 6241
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6241}=79$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-79)-79}{2*15}=\frac{0}{30}
=0
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-79)+79}{2*15}=\frac{158}{30}
=5+4/15
$