-2/x-5=x

Solution for -2/x-5=x equation:

-2/x-5=x

We move all terms to the left:

-2/x-5-(x)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

-1x-2/x-5=0

We multiply all the terms by the denominator


-1x*x-5*x-2=0

We add all the numbers together, and all the variables

-5x-1x*x-2=0

Wy multiply elements

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

a = -1; b = -5; c = -2;
Δ = b2-4ac
Δ = -52-4·(-1)·(-2)
Δ = 17
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{17}}{2*-1}=\frac{5-\sqrt{17}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{17}}{2*-1}=\frac{5+\sqrt{17}}{-2}
$