4/3x-5/8=1/9x

Solution for 4/3x-5/8=1/9x equation:

4/3x-5/8=1/9x

We move all terms to the left:

4/3x-5/8-(1/9x)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 9x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

4/3x-(+1/9x)-5/8=0

We get rid of parentheses

4/3x-1/9x-5/8=0

We calculate fractions


(-1215x^2)/1728x^2+2304x/1728x^2+(-192x)/1728x^2=0

We multiply all the terms by the denominator


(-1215x^2)+2304x+(-192x)=0

We get rid of parentheses

-1215x^2+2304x-192x=0

We add all the numbers together, and all the variables

-1215x^2+2112x=0

a = -1215; b = 2112; c = 0;
Δ = b2-4ac
Δ = 21122-4·(-1215)·0
Δ = 4460544
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4460544}=2112$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2112)-2112}{2*-1215}=\frac{-4224}{-2430}
=1+299/405
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2112)+2112}{2*-1215}=\frac{0}{-2430}
=0
$