3x+17=6/x

Solution for 3x+17=6/x equation:

3x+17=6/x

We move all terms to the left:

3x+17-(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

3x-(+6/x)+17=0

We get rid of parentheses

3x-6/x+17=0

We multiply all the terms by the denominator


3x*x+17*x-6=0

We add all the numbers together, and all the variables

17x+3x*x-6=0

Wy multiply elements

3x^2+17x-6=0

a = 3; b = 17; c = -6;
Δ = b2-4ac
Δ = 172-4·3·(-6)
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-19}{2*3}=\frac{-36}{6}
=-6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+19}{2*3}=\frac{2}{6}
=1/3
$