1/8p+1=1/6p-1

Solution for 1/8p+1=1/6p-1 equation:

1/8p+1=1/6p-1

We move all terms to the left:

1/8p+1-(1/6p-1)=0


Domain of the equation: 8p!=0

p!=0/8

p!=0

p∈R



Domain of the equation: 6p-1)!=0

p∈R


We get rid of parentheses

1/8p-1/6p+1+1=0

We calculate fractions


6p/48p^2+(-8p)/48p^2+1+1=0

We add all the numbers together, and all the variables

6p/48p^2+(-8p)/48p^2+2=0

We multiply all the terms by the denominator


6p+(-8p)+2*48p^2=0

Wy multiply elements

96p^2+6p+(-8p)=0

We get rid of parentheses

96p^2+6p-8p=0

We add all the numbers together, and all the variables

96p^2-2p=0

a = 96; b = -2; c = 0;
Δ = b2-4ac
Δ = -22-4·96·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2}{2*96}=\frac{0}{192}
=0
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2}{2*96}=\frac{4}{192}
=1/48
$