-17-2x=6/x

Solution for -17-2x=6/x equation:

-17-2x=6/x

We move all terms to the left:

-17-2x-(6/x)=0


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-2x-(+6/x)-17=0

We get rid of parentheses

-2x-6/x-17=0

We multiply all the terms by the denominator


-2x*x-17*x-6=0

We add all the numbers together, and all the variables

-17x-2x*x-6=0

Wy multiply elements

-2x^2-17x-6=0

a = -2; b = -17; c = -6;
Δ = b2-4ac
Δ = -172-4·(-2)·(-6)
Δ = 241
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{-(-17)-\sqrt{241}}{2*-2}=\frac{17-\sqrt{241}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+\sqrt{241}}{2*-2}=\frac{17+\sqrt{241}}{-4}
$