x=12/x-11

Solution for x=12/x-11 equation:

x=12/x-11

We move all terms to the left:

x-(12/x-11)=0


Domain of the equation: x-11)!=0

x∈R


We get rid of parentheses

x-12/x+11=0

We multiply all the terms by the denominator


x*x+11*x-12=0

We add all the numbers together, and all the variables

11x+x*x-12=0

Wy multiply elements

x^2+11x-12=0

a = 1; b = 11; c = -12;
Δ = b2-4ac
Δ = 112-4·1·(-12)
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-13}{2*1}=\frac{-24}{2}
=-12
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+13}{2*1}=\frac{2}{2}
=1
$