1/11x+9=-x-12

Solution for 1/11x+9=-x-12 equation:

1/11x+9=-x-12

We move all terms to the left:

1/11x+9-(-x-12)=0


Domain of the equation: 11x!=0

x!=0/11

x!=0

x∈R


We add all the numbers together, and all the variables

1/11x-(-1x-12)+9=0

We get rid of parentheses

1/11x+1x+12+9=0

We multiply all the terms by the denominator


1x*11x+12*11x+9*11x+1=0

Wy multiply elements

11x^2+132x+99x+1=0

We add all the numbers together, and all the variables

11x^2+231x+1=0

a = 11; b = 231; c = +1;
Δ = b2-4ac
Δ = 2312-4·11·1
Δ = 53317
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(231)-\sqrt{53317}}{2*11}=\frac{-231-\sqrt{53317}}{22}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(231)+\sqrt{53317}}{2*11}=\frac{-231+\sqrt{53317}}{22}
$