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

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

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

We move all terms to the left:

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


Domain of the equation: 2p)!=0

p!=0/1

p!=0

p∈R



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

We move all terms containing p to the left, all other terms to the right

-p))!=-3

p!=-3/1

p!=-3

p∈R


We add all the numbers together, and all the variables

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

We multiply parentheses

-10p-(3(-1p+2/3))+8=0

We multiply all the terms by the denominator


-10p*3))-(3(-1p+2+8*3))=0

We add all the numbers together, and all the variables

-10p*3))-(3(-1p+26))=0

We add all the numbers together, and all the variables

-1p-10p*3))-(3(=0

Wy multiply elements

-30p^2-1p=0

a = -30; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·(-30)·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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