2/3x+5/8=7/9x

Solution for 2/3x+5/8=7/9x equation:

2/3x+5/8=7/9x

We move all terms to the left:

2/3x+5/8-(7/9x)=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

2/3x-(+7/9x)+5/8=0

We get rid of parentheses

2/3x-7/9x+5/8=0

We calculate fractions


1215x^2/1728x^2+1152x/1728x^2+(-1344x)/1728x^2=0

We multiply all the terms by the denominator


1215x^2+1152x+(-1344x)=0

We get rid of parentheses

1215x^2+1152x-1344x=0

We add all the numbers together, and all the variables

1215x^2-192x=0

a = 1215; b = -192; c = 0;
Δ = b2-4ac
Δ = -1922-4·1215·0
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*1215}=\frac{0}{2430}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-192)+192}{2*1215}=\frac{384}{2430}
=64/405
$