5/9p+8=1/6p+1

Solution for 5/9p+8=1/6p+1 equation:

5/9p+8=1/6p+1

We move all terms to the left:

5/9p+8-(1/6p+1)=0


Domain of the equation: 9p!=0

p!=0/9

p!=0

p∈R



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

p∈R


We get rid of parentheses

5/9p-1/6p-1+8=0

We calculate fractions


30p/54p^2+(-9p)/54p^2-1+8=0

We add all the numbers together, and all the variables

30p/54p^2+(-9p)/54p^2+7=0

We multiply all the terms by the denominator


30p+(-9p)+7*54p^2=0

Wy multiply elements

378p^2+30p+(-9p)=0

We get rid of parentheses

378p^2+30p-9p=0

We add all the numbers together, and all the variables

378p^2+21p=0

a = 378; b = 21; c = 0;
Δ = b2-4ac
Δ = 212-4·378·0
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-21}{2*378}=\frac{-42}{756}
=-1/18
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+21}{2*378}=\frac{0}{756}
=0
$