15-1/p=-1+3/5p

Solution for 15-1/p=-1+3/5p equation:

15-1/p=-1+3/5p

We move all terms to the left:

15-1/p-(-1+3/5p)=0


Domain of the equation: p!=0

p∈R



Domain of the equation: 5p)!=0

p!=0/1

p!=0

p∈R


We add all the numbers together, and all the variables

-1/p-(3/5p-1)+15=0

We get rid of parentheses

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

We calculate fractions


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

We add all the numbers together, and all the variables

(-5p)/5p^2+(-3p)/5p^2+16=0

We multiply all the terms by the denominator


(-5p)+(-3p)+16*5p^2=0

Wy multiply elements

80p^2+(-5p)+(-3p)=0

We get rid of parentheses

80p^2-5p-3p=0

We add all the numbers together, and all the variables

80p^2-8p=0

a = 80; b = -8; c = 0;
Δ = b2-4ac
Δ = -82-4·80·0
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*80}=\frac{0}{160}
=0
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+8}{2*80}=\frac{16}{160}
=1/10
$