3/2p=2/3p+5

Solution for 3/2p=2/3p+5 equation:

3/2p=2/3p+5

We move all terms to the left:

3/2p-(2/3p+5)=0


Domain of the equation: 2p!=0

p!=0/2

p!=0

p∈R



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

p∈R


We get rid of parentheses

3/2p-2/3p-5=0

We calculate fractions


9p/6p^2+(-4p)/6p^2-5=0

We multiply all the terms by the denominator


9p+(-4p)-5*6p^2=0

Wy multiply elements

-30p^2+9p+(-4p)=0

We get rid of parentheses

-30p^2+9p-4p=0

We add all the numbers together, and all the variables

-30p^2+5p=0

a = -30; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·(-30)·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*-30}=\frac{-10}{-60}
=1/6
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*-30}=\frac{0}{-60}
=0
$