3/4p-4/5=2/3p-1

Solution for 3/4p-4/5=2/3p-1 equation:

3/4p-4/5=2/3p-1

We move all terms to the left:

3/4p-4/5-(2/3p-1)=0


Domain of the equation: 4p!=0

p!=0/4

p!=0

p∈R



Domain of the equation: 3p-1)!=0

p∈R


We get rid of parentheses

3/4p-2/3p+1-4/5=0

We calculate fractions


(-144p^2)/300p^2+225p/300p^2+(-200p)/300p^2+1=0

We multiply all the terms by the denominator


(-144p^2)+225p+(-200p)+1*300p^2=0

Wy multiply elements

(-144p^2)+300p^2+225p+(-200p)=0

We get rid of parentheses

-144p^2+300p^2+225p-200p=0

We add all the numbers together, and all the variables

156p^2+25p=0

a = 156; b = 25; c = 0;
Δ = b2-4ac
Δ = 252-4·156·0
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*156}=\frac{-50}{312}
=-25/156
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+25}{2*156}=\frac{0}{312}
=0
$