1/2p-3=2-2/3p

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

1/2p-3=2-2/3p

We move all terms to the left:

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


Domain of the equation: 2p!=0

p!=0/2

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

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

We get rid of parentheses

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

We calculate fractions


3p/6p^2+4p/6p^2-2-3=0

We add all the numbers together, and all the variables

3p/6p^2+4p/6p^2-5=0

We multiply all the terms by the denominator


3p+4p-5*6p^2=0

We add all the numbers together, and all the variables

7p-5*6p^2=0

Wy multiply elements

-30p^2+7p=0

a = -30; b = 7; c = 0;
Δ = b2-4ac
Δ = 72-4·(-30)·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-7}{2*-30}=\frac{-14}{-60}
=7/30
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+7}{2*-30}=\frac{0}{-60}
=0
$