6/3p+1=9/5p-3

Solution for 6/3p+1=9/5p-3 equation:

6/3p+1=9/5p-3

We move all terms to the left:

6/3p+1-(9/5p-3)=0


Domain of the equation: 3p!=0

p!=0/3

p!=0

p∈R



Domain of the equation: 5p-3)!=0

p∈R


We get rid of parentheses

6/3p-9/5p+3+1=0

We calculate fractions


30p/15p^2+(-27p)/15p^2+3+1=0

We add all the numbers together, and all the variables

30p/15p^2+(-27p)/15p^2+4=0

We multiply all the terms by the denominator


30p+(-27p)+4*15p^2=0

Wy multiply elements

60p^2+30p+(-27p)=0

We get rid of parentheses

60p^2+30p-27p=0

We add all the numbers together, and all the variables

60p^2+3p=0

a = 60; b = 3; c = 0;
Δ = b2-4ac
Δ = 32-4·60·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3}{2*60}=\frac{-6}{120}
=-1/20
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3}{2*60}=\frac{0}{120}
=0
$