17/x-6x=14

Solution for 17/x-6x=14 equation:

17/x-6x=14

We move all terms to the left:

17/x-6x-(14)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

-6x+17/x-14=0

We multiply all the terms by the denominator


-6x*x-14*x+17=0

We add all the numbers together, and all the variables

-14x-6x*x+17=0

Wy multiply elements

-6x^2-14x+17=0

a = -6; b = -14; c = +17;
Δ = b2-4ac
Δ = -142-4·(-6)·17
Δ = 604
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:

$\sqrt{\Delta}=\sqrt{604}=\sqrt{4*151}=\sqrt{4}*\sqrt{151}=2\sqrt{151}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{151}}{2*-6}=\frac{14-2\sqrt{151}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{151}}{2*-6}=\frac{14+2\sqrt{151}}{-12}
$