6-(5/x+1)=x

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

6-(5/x+1)=x

We move all terms to the left:

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


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

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


-1x*x-1*x+6*x-5=0

We add all the numbers together, and all the variables

5x-1x*x-5=0

Wy multiply elements

-1x^2+5x-5=0

a = -1; b = 5; c = -5;
Δ = b2-4ac
Δ = 52-4·(-1)·(-5)
Δ = 5
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{-(5)-\sqrt{5}}{2*-1}=\frac{-5-\sqrt{5}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{5}}{2*-1}=\frac{-5+\sqrt{5}}{-2}
$