3/9p-3=1/8p-5

Solution for 3/9p-3=1/8p-5 equation:

3/9p-3=1/8p-5

We move all terms to the left:

3/9p-3-(1/8p-5)=0


Domain of the equation: 9p!=0

p!=0/9

p!=0

p∈R



Domain of the equation: 8p-5)!=0

p∈R


We get rid of parentheses

3/9p-1/8p+5-3=0

We calculate fractions


24p/72p^2+(-9p)/72p^2+5-3=0

We add all the numbers together, and all the variables

24p/72p^2+(-9p)/72p^2+2=0

We multiply all the terms by the denominator


24p+(-9p)+2*72p^2=0

Wy multiply elements

144p^2+24p+(-9p)=0

We get rid of parentheses

144p^2+24p-9p=0

We add all the numbers together, and all the variables

144p^2+15p=0

a = 144; b = 15; c = 0;
Δ = b2-4ac
Δ = 152-4·144·0
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-15}{2*144}=\frac{-30}{288}
=-5/48
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+15}{2*144}=\frac{0}{288}
=0
$