1/2p=200-1/3p

Solution for 1/2p=200-1/3p equation:

1/2p=200-1/3p

We move all terms to the left:

1/2p-(200-1/3p)=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-(-1/3p+200)=0

We get rid of parentheses

1/2p+1/3p-200=0

We calculate fractions


3p/6p^2+2p/6p^2-200=0

We multiply all the terms by the denominator


3p+2p-200*6p^2=0

We add all the numbers together, and all the variables

5p-200*6p^2=0

Wy multiply elements

-1200p^2+5p=0

a = -1200; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·(-1200)·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*-1200}=\frac{-10}{-2400}
=1/240
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*-1200}=\frac{0}{-2400}
=0
$