1/3p+1/5p=1

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

1/3p+1/5p=1

We move all terms to the left:

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


Domain of the equation: 3p!=0

p!=0/3

p!=0

p∈R



Domain of the equation: 5p!=0

p!=0/5

p!=0

p∈R


We calculate fractions


5p/15p^2+3p/15p^2-1=0

We multiply all the terms by the denominator


5p+3p-1*15p^2=0

We add all the numbers together, and all the variables

8p-1*15p^2=0

Wy multiply elements

-15p^2+8p=0

a = -15; b = 8; c = 0;
Δ = b2-4ac
Δ = 82-4·(-15)·0
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-8}{2*-15}=\frac{-16}{-30}
=8/15
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8}{2*-15}=\frac{0}{-30}
=0
$