2/3p-4=4/5p

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

2/3p-4=4/5p

We move all terms to the left:

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


Domain of the equation: 3p!=0

p!=0/3

p!=0

p∈R



Domain of the equation: 5p)!=0

p!=0/1

p!=0

p∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


10p/15p^2+(-12p)/15p^2-4=0

We multiply all the terms by the denominator


10p+(-12p)-4*15p^2=0

Wy multiply elements

-60p^2+10p+(-12p)=0

We get rid of parentheses

-60p^2+10p-12p=0

We add all the numbers together, and all the variables

-60p^2-2p=0

a = -60; b = -2; c = 0;
Δ = b2-4ac
Δ = -22-4·(-60)·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2}{2*-60}=\frac{0}{-120}
=0
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2}{2*-60}=\frac{4}{-120}
=-1/30
$