1/2p+1/5p=2/3

Solution for 1/2p+1/5p=2/3 equation:

1/2p+1/5p=2/3

We move all terms to the left:

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


Domain of the equation: 2p!=0

p!=0/2

p!=0

p∈R



Domain of the equation: 5p!=0

p!=0/5

p!=0

p∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

1/2p+1/5p-2/3=0

We calculate fractions


(-100p^2)/90p^2+45p/90p^2+18p/90p^2=0

We multiply all the terms by the denominator


(-100p^2)+45p+18p=0

We add all the numbers together, and all the variables

(-100p^2)+63p=0

We get rid of parentheses

-100p^2+63p=0

a = -100; b = 63; c = 0;
Δ = b2-4ac
Δ = 632-4·(-100)·0
Δ = 3969
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3969}=63$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(63)-63}{2*-100}=\frac{-126}{-200}
=63/100
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(63)+63}{2*-100}=\frac{0}{-200}
=0
$