5-1/3p=4/9p+22

Solution for 5-1/3p=4/9p+22 equation:

5-1/3p=4/9p+22

We move all terms to the left:

5-1/3p-(4/9p+22)=0


Domain of the equation: 3p!=0

p!=0/3

p!=0

p∈R



Domain of the equation: 9p+22)!=0

p∈R


We get rid of parentheses

-1/3p-4/9p-22+5=0

We calculate fractions


(-9p)/27p^2+(-12p)/27p^2-22+5=0

We add all the numbers together, and all the variables

(-9p)/27p^2+(-12p)/27p^2-17=0

We multiply all the terms by the denominator


(-9p)+(-12p)-17*27p^2=0

Wy multiply elements

-459p^2+(-9p)+(-12p)=0

We get rid of parentheses

-459p^2-9p-12p=0

We add all the numbers together, and all the variables

-459p^2-21p=0

a = -459; b = -21; c = 0;
Δ = b2-4ac
Δ = -212-4·(-459)·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*-459}=\frac{0}{-918}
=0
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+21}{2*-459}=\frac{42}{-918}
=-7/153
$