2/3p-3/5=1/2p+1

Solution for 2/3p-3/5=1/2p+1 equation:

2/3p-3/5=1/2p+1

We move all terms to the left:

2/3p-3/5-(1/2p+1)=0


Domain of the equation: 3p!=0

p!=0/3

p!=0

p∈R



Domain of the equation: 2p+1)!=0

p∈R


We get rid of parentheses

2/3p-1/2p-1-3/5=0

We calculate fractions


(-36p^2)/150p^2+100p/150p^2+(-75p)/150p^2-1=0

We multiply all the terms by the denominator


(-36p^2)+100p+(-75p)-1*150p^2=0

Wy multiply elements

(-36p^2)-150p^2+100p+(-75p)=0

We get rid of parentheses

-36p^2-150p^2+100p-75p=0

We add all the numbers together, and all the variables

-186p^2+25p=0

a = -186; b = 25; c = 0;
Δ = b2-4ac
Δ = 252-4·(-186)·0
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(25)-25}{2*-186}=\frac{-50}{-372}
=25/186
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+25}{2*-186}=\frac{0}{-372}
=0
$