3/2p+5=1/9p

Solution for 3/2p+5=1/9p equation:

3/2p+5=1/9p

We move all terms to the left:

3/2p+5-(1/9p)=0


Domain of the equation: 2p!=0

p!=0/2

p!=0

p∈R



Domain of the equation: 9p)!=0

p!=0/1

p!=0

p∈R


We add all the numbers together, and all the variables

3/2p-(+1/9p)+5=0

We get rid of parentheses

3/2p-1/9p+5=0

We calculate fractions


27p/18p^2+(-2p)/18p^2+5=0

We multiply all the terms by the denominator


27p+(-2p)+5*18p^2=0

Wy multiply elements

90p^2+27p+(-2p)=0

We get rid of parentheses

90p^2+27p-2p=0

We add all the numbers together, and all the variables

90p^2+25p=0

a = 90; b = 25; c = 0;
Δ = b2-4ac
Δ = 252-4·90·0
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(25)-25}{2*90}=\frac{-50}{180}
=-5/18
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+25}{2*90}=\frac{0}{180}
=0
$