x+6/x-1=5

Solution for x+6/x-1=5 equation:

x+6/x-1=5

We move all terms to the left:

x+6/x-1-(5)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

x+6/x-6=0

We multiply all the terms by the denominator


x*x-6*x+6=0

We add all the numbers together, and all the variables

-6x+x*x+6=0

Wy multiply elements

x^2-6x+6=0

a = 1; b = -6; c = +6;
Δ = b2-4ac
Δ = -62-4·1·6
Δ = 12
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:

$\sqrt{\Delta}=\sqrt{12}=\sqrt{4*3}=\sqrt{4}*\sqrt{3}=2\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{3}}{2*1}=\frac{6-2\sqrt{3}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{3}}{2*1}=\frac{6+2\sqrt{3}}{2}
$