(6/x-1)+x=11

Solution for (6/x-1)+x=11 equation:

(6/x-1)+x=11

We move all terms to the left:

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


Domain of the equation: x-1)!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

x+6/x-1-11=0

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

-12x+x*x+6=0

Wy multiply elements

x^2-12x+6=0

a = 1; b = -12; c = +6;
Δ = b2-4ac
Δ = -122-4·1·6
Δ = 120
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{120}=\sqrt{4*30}=\sqrt{4}*\sqrt{30}=2\sqrt{30}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{30}}{2*1}=\frac{12-2\sqrt{30}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{30}}{2*1}=\frac{12+2\sqrt{30}}{2}
$