1/3p+3/9=11/18p

Solution for 1/3p+3/9=11/18p equation:

1/3p+3/9=11/18p

We move all terms to the left:

1/3p+3/9-(11/18p)=0


Domain of the equation: 3p!=0

p!=0/3

p!=0

p∈R



Domain of the equation: 18p)!=0

p!=0/1

p!=0

p∈R


We add all the numbers together, and all the variables

1/3p-(+11/18p)+3/9=0

We get rid of parentheses

1/3p-11/18p+3/9=0

We calculate fractions


162p^2/4374p^2+1458p/4374p^2+(-2673p)/4374p^2=0

We multiply all the terms by the denominator


162p^2+1458p+(-2673p)=0

We get rid of parentheses

162p^2+1458p-2673p=0

We add all the numbers together, and all the variables

162p^2-1215p=0

a = 162; b = -1215; c = 0;
Δ = b2-4ac
Δ = -12152-4·162·0
Δ = 1476225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1476225}=1215$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1215)-1215}{2*162}=\frac{0}{324}
=0
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1215)+1215}{2*162}=\frac{2430}{324}
=7+1/2
$