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

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

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

We move all terms to the left:

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


Domain of the equation: 2p!=0

p!=0/2

p!=0

p∈R



Domain of the equation: 3p)!=0

p!=0/1

p!=0

p∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


15p/6p^2+(-2p)/6p^2-5-9=0

We add all the numbers together, and all the variables

15p/6p^2+(-2p)/6p^2-14=0

We multiply all the terms by the denominator


15p+(-2p)-14*6p^2=0

Wy multiply elements

-84p^2+15p+(-2p)=0

We get rid of parentheses

-84p^2+15p-2p=0

We add all the numbers together, and all the variables

-84p^2+13p=0

a = -84; b = 13; c = 0;
Δ = b2-4ac
Δ = 132-4·(-84)·0
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-13}{2*-84}=\frac{-26}{-168}
=13/84
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+13}{2*-84}=\frac{0}{-168}
=0
$