x/6x+2=3x+17

Solution for x/6x+2=3x+17 equation:

x/6x+2=3x+17

We move all terms to the left:

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


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

-18x^2+x-102x+12x=0

We add all the numbers together, and all the variables

-18x^2-89x=0

a = -18; b = -89; c = 0;
Δ = b2-4ac
Δ = -892-4·(-18)·0
Δ = 7921
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{7921}=89$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-89)-89}{2*-18}=\frac{0}{-36}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-89)+89}{2*-18}=\frac{178}{-36}
=-4+17/18
$