3/5p+1=1/3p-4

Solution for 3/5p+1=1/3p-4 equation:

3/5p+1=1/3p-4

We move all terms to the left:

3/5p+1-(1/3p-4)=0


Domain of the equation: 5p!=0

p!=0/5

p!=0

p∈R



Domain of the equation: 3p-4)!=0

p∈R


We get rid of parentheses

3/5p-1/3p+4+1=0

We calculate fractions


9p/15p^2+(-5p)/15p^2+4+1=0

We add all the numbers together, and all the variables

9p/15p^2+(-5p)/15p^2+5=0

We multiply all the terms by the denominator


9p+(-5p)+5*15p^2=0

Wy multiply elements

75p^2+9p+(-5p)=0

We get rid of parentheses

75p^2+9p-5p=0

We add all the numbers together, and all the variables

75p^2+4p=0

a = 75; b = 4; c = 0;
Δ = b2-4ac
Δ = 42-4·75·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4}{2*75}=\frac{-8}{150}
=-4/75
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4}{2*75}=\frac{0}{150}
=0
$