x=x/9x-7

Solution for x=x/9x-7 equation:

x=x/9x-7

We move all terms to the left:

x-(x/9x-7)=0


Domain of the equation: 9x-7)!=0

x∈R


We get rid of parentheses

x-x/9x+7=0

We multiply all the terms by the denominator


x*9x-x+7*9x=0

We add all the numbers together, and all the variables

-1x+x*9x+7*9x=0

Wy multiply elements

9x^2-1x+63x=0

We add all the numbers together, and all the variables

9x^2+62x=0

a = 9; b = 62; c = 0;
Δ = b2-4ac
Δ = 622-4·9·0
Δ = 3844
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3844}=62$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(62)-62}{2*9}=\frac{-124}{18}
=-6+8/9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(62)+62}{2*9}=\frac{0}{18}
=0
$