11/15p-1/6=4/9p-1

Solution for 11/15p-1/6=4/9p-1 equation:

11/15p-1/6=4/9p-1

We move all terms to the left:

11/15p-1/6-(4/9p-1)=0


Domain of the equation: 15p!=0

p!=0/15

p!=0

p∈R



Domain of the equation: 9p-1)!=0

p∈R


We get rid of parentheses

11/15p-4/9p+1-1/6=0

We calculate fractions


(-1215p^2)/4860p^2+3564p/4860p^2+(-2160p)/4860p^2+1=0

We multiply all the terms by the denominator


(-1215p^2)+3564p+(-2160p)+1*4860p^2=0

Wy multiply elements

(-1215p^2)+4860p^2+3564p+(-2160p)=0

We get rid of parentheses

-1215p^2+4860p^2+3564p-2160p=0

We add all the numbers together, and all the variables

3645p^2+1404p=0

a = 3645; b = 1404; c = 0;
Δ = b2-4ac
Δ = 14042-4·3645·0
Δ = 1971216
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1971216}=1404$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1404)-1404}{2*3645}=\frac{-2808}{7290}
=-52/135
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1404)+1404}{2*3645}=\frac{0}{7290}
=0
$