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

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

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

We move all terms to the left:

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


Domain of the equation: 3p!=0

p!=0/3

p!=0

p∈R



Domain of the equation: 3p)!=0

p!=0/1

p!=0

p∈R


We add all the numbers together, and all the variables

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


-2p*3p-5*3p+2-4=0

We add all the numbers together, and all the variables

-2p*3p-5*3p-2=0

Wy multiply elements

-6p^2-15p-2=0

a = -6; b = -15; c = -2;
Δ = b2-4ac
Δ = -152-4·(-6)·(-2)
Δ = 177
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-\sqrt{177}}{2*-6}=\frac{15-\sqrt{177}}{-12}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+\sqrt{177}}{2*-6}=\frac{15+\sqrt{177}}{-12}
$