6x-4=17/x

Solution for 6x-4=17/x equation:

6x-4=17/x

We move all terms to the left:

6x-4-(17/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

6x-(+17/x)-4=0

We get rid of parentheses

6x-17/x-4=0

We multiply all the terms by the denominator


6x*x-4*x-17=0

We add all the numbers together, and all the variables

-4x+6x*x-17=0

Wy multiply elements

6x^2-4x-17=0

a = 6; b = -4; c = -17;
Δ = b2-4ac
Δ = -42-4·6·(-17)
Δ = 424
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:

$\sqrt{\Delta}=\sqrt{424}=\sqrt{4*106}=\sqrt{4}*\sqrt{106}=2\sqrt{106}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{106}}{2*6}=\frac{4-2\sqrt{106}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{106}}{2*6}=\frac{4+2\sqrt{106}}{12}
$