6/2x-51/3=3x-17

Solution for 6/2x-51/3=3x-17 equation:

6/2x-51/3=3x-17

We move all terms to the left:

6/2x-51/3-(3x-17)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

6/2x-(3x-17)-17=0

We get rid of parentheses

6/2x-3x+17-17=0

We multiply all the terms by the denominator


-3x*2x+17*2x-17*2x+6=0

Wy multiply elements

-6x^2+34x-34x+6=0

We add all the numbers together, and all the variables

-6x^2+6=0

a = -6; b = 0; c = +6;
Δ = b2-4ac
Δ = 02-4·(-6)·6
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12}{2*-6}=\frac{-12}{-12}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12}{2*-6}=\frac{12}{-12}
=-1
$