11x/9x=-x-6

Solution for 11x/9x=-x-6 equation:

11x/9x=-x-6

We move all terms to the left:

11x/9x-(-x-6)=0


Domain of the equation: 9x!=0

x!=0/9

x!=0

x∈R


We add all the numbers together, and all the variables

11x/9x-(-1x-6)=0

We get rid of parentheses

11x/9x+1x+6=0

We multiply all the terms by the denominator


11x+1x*9x+6*9x=0

Wy multiply elements

9x^2+11x+54x=0

We add all the numbers together, and all the variables

9x^2+65x=0

a = 9; b = 65; c = 0;
Δ = b2-4ac
Δ = 652-4·9·0
Δ = 4225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4225}=65$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(65)-65}{2*9}=\frac{-130}{18}
=-7+2/9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(65)+65}{2*9}=\frac{0}{18}
=0
$