8/9x=2-17/18x

Solution for 8/9x=2-17/18x equation:

8/9x=2-17/18x

We move all terms to the left:

8/9x-(2-17/18x)=0


Domain of the equation: 9x!=0

x!=0/9

x!=0

x∈R



Domain of the equation: 18x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

8/9x-(-17/18x+2)=0

We get rid of parentheses

8/9x+17/18x-2=0

We calculate fractions


144x/162x^2+153x/162x^2-2=0

We multiply all the terms by the denominator


144x+153x-2*162x^2=0

We add all the numbers together, and all the variables

297x-2*162x^2=0

Wy multiply elements

-324x^2+297x=0

a = -324; b = 297; c = 0;
Δ = b2-4ac
Δ = 2972-4·(-324)·0
Δ = 88209
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{88209}=297$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(297)-297}{2*-324}=\frac{-594}{-648}
=11/12
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(297)+297}{2*-324}=\frac{0}{-648}
=0
$