2/3p-2/5=5/9p+4

Solution for 2/3p-2/5=5/9p+4 equation:

2/3p-2/5=5/9p+4

We move all terms to the left:

2/3p-2/5-(5/9p+4)=0


Domain of the equation: 3p!=0

p!=0/3

p!=0

p∈R



Domain of the equation: 9p+4)!=0

p∈R


We get rid of parentheses

2/3p-5/9p-4-2/5=0

We calculate fractions


(-486p^2)/675p^2+450p/675p^2+(-375p)/675p^2-4=0

We multiply all the terms by the denominator


(-486p^2)+450p+(-375p)-4*675p^2=0

Wy multiply elements

(-486p^2)-2700p^2+450p+(-375p)=0

We get rid of parentheses

-486p^2-2700p^2+450p-375p=0

We add all the numbers together, and all the variables

-3186p^2+75p=0

a = -3186; b = 75; c = 0;
Δ = b2-4ac
Δ = 752-4·(-3186)·0
Δ = 5625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5625}=75$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(75)-75}{2*-3186}=\frac{-150}{-6372}
=25/1062
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(75)+75}{2*-3186}=\frac{0}{-6372}
=0
$