1/3p+80=-1/2p+120

Solution for 1/3p+80=-1/2p+120 equation:

1/3p+80=-1/2p+120

We move all terms to the left:

1/3p+80-(-1/2p+120)=0


Domain of the equation: 3p!=0

p!=0/3

p!=0

p∈R



Domain of the equation: 2p+120)!=0

p∈R


We get rid of parentheses

1/3p+1/2p-120+80=0

We calculate fractions


2p/6p^2+3p/6p^2-120+80=0

We add all the numbers together, and all the variables

2p/6p^2+3p/6p^2-40=0

We multiply all the terms by the denominator


2p+3p-40*6p^2=0

We add all the numbers together, and all the variables

5p-40*6p^2=0

Wy multiply elements

-240p^2+5p=0

a = -240; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·(-240)·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5}{2*-240}=\frac{-10}{-480}
=1/48
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*-240}=\frac{0}{-480}
=0
$