4/x-1+x=11

Solution for 4/x-1+x=11 equation:

4/x-1+x=11

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

x+4/x-12=0

We multiply all the terms by the denominator


x*x-12*x+4=0

We add all the numbers together, and all the variables

-12x+x*x+4=0

Wy multiply elements

x^2-12x+4=0

a = 1; b = -12; c = +4;
Δ = b2-4ac
Δ = -122-4·1·4
Δ = 128
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:

$\sqrt{\Delta}=\sqrt{128}=\sqrt{64*2}=\sqrt{64}*\sqrt{2}=8\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-8\sqrt{2}}{2*1}=\frac{12-8\sqrt{2}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+8\sqrt{2}}{2*1}=\frac{12+8\sqrt{2}}{2}
$