x=8/9x+2

Solution for x=8/9x+2 equation:

x=8/9x+2

We move all terms to the left:

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


Domain of the equation: 9x+2)!=0

x∈R


We get rid of parentheses

x-8/9x-2=0

We multiply all the terms by the denominator


x*9x-2*9x-8=0

Wy multiply elements

9x^2-18x-8=0

a = 9; b = -18; c = -8;
Δ = b2-4ac
Δ = -182-4·9·(-8)
Δ = 612
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{612}=\sqrt{36*17}=\sqrt{36}*\sqrt{17}=6\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-6\sqrt{17}}{2*9}=\frac{18-6\sqrt{17}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+6\sqrt{17}}{2*9}=\frac{18+6\sqrt{17}}{18}
$