4/9p-2/3p=4

Solution for 4/9p-2/3p=4 equation:

4/9p-2/3p=4

We move all terms to the left:

4/9p-2/3p-(4)=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 calculate fractions


12p/27p^2+(-18p)/27p^2-4=0

We multiply all the terms by the denominator


12p+(-18p)-4*27p^2=0

Wy multiply elements

-108p^2+12p+(-18p)=0

We get rid of parentheses

-108p^2+12p-18p=0

We add all the numbers together, and all the variables

-108p^2-6p=0

a = -108; b = -6; c = 0;
Δ = b2-4ac
Δ = -62-4·(-108)·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6}{2*-108}=\frac{0}{-216}
=0
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6}{2*-108}=\frac{12}{-216}
=-1/18
$