5/9x-2/3x=3/8

Solution for 5/9x-2/3x=3/8 equation:

5/9x-2/3x=3/8

We move all terms to the left:

5/9x-2/3x-(3/8)=0


Domain of the equation: 9x!=0

x!=0/9

x!=0

x∈R



Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

5/9x-2/3x-(+3/8)=0

We get rid of parentheses

5/9x-2/3x-3/8=0

We calculate fractions


(-243x^2)/1728x^2+960x/1728x^2+(-1152x)/1728x^2=0

We multiply all the terms by the denominator


(-243x^2)+960x+(-1152x)=0

We get rid of parentheses

-243x^2+960x-1152x=0

We add all the numbers together, and all the variables

-243x^2-192x=0

a = -243; b = -192; c = 0;
Δ = b2-4ac
Δ = -1922-4·(-243)·0
Δ = 36864
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36864}=192$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-192)-192}{2*-243}=\frac{0}{-486}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-192)+192}{2*-243}=\frac{384}{-486}
=-64/81
$