x=-5/9x+2=

Solution for x=-5/9x+2= equation:

x=-5/9x+2=

We move all terms to the left:

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


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

x∈R


We get rid of parentheses

x+5/9x-2=0

We multiply all the terms by the denominator


x*9x-2*9x+5=0

Wy multiply elements

9x^2-18x+5=0

a = 9; b = -18; c = +5;
Δ = b2-4ac
Δ = -182-4·9·5
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-12}{2*9}=\frac{6}{18}
=1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+12}{2*9}=\frac{30}{18}
=1+2/3
$