4/9p+1/3p-1/2=11/6

Solution for 4/9p+1/3p-1/2=11/6 equation:

4/9p+1/3p-1/2=11/6

We move all terms to the left:

4/9p+1/3p-1/2-(11/6)=0


Domain of the equation: 9p!=0

p!=0/9

p!=0

p∈R



Domain of the equation: 3p!=0

p!=0/3

p!=0

p∈R


We add all the numbers together, and all the variables

4/9p+1/3p-1/2-(+11/6)=0

We get rid of parentheses

4/9p+1/3p-1/2-11/6=0

We calculate fractions


(-486p^2)/648p^2+(-1782p^2)/648p^2+288p/648p^2+216p/648p^2=0

We multiply all the terms by the denominator


(-486p^2)+(-1782p^2)+288p+216p=0

We add all the numbers together, and all the variables

(-486p^2)+(-1782p^2)+504p=0

We get rid of parentheses

-486p^2-1782p^2+504p=0

We add all the numbers together, and all the variables

-2268p^2+504p=0

a = -2268; b = 504; c = 0;
Δ = b2-4ac
Δ = 5042-4·(-2268)·0
Δ = 254016
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{254016}=504$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(504)-504}{2*-2268}=\frac{-1008}{-4536}
=2/9
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(504)+504}{2*-2268}=\frac{0}{-4536}
=0
$