X/3x+6=2x-1

Solution for X/3x+6=2x-1 equation:

X/3X+6=2X-1

We move all terms to the left:

X/3X+6-(2X-1)=0


Domain of the equation: 3X!=0

X!=0/3

X!=0

X∈R


We get rid of parentheses

X/3X-2X+1+6=0

We multiply all the terms by the denominator


X-2X*3X+1*3X+6*3X=0

Wy multiply elements

-6X^2+X+3X+18X=0

We add all the numbers together, and all the variables

-6X^2+22X=0

a = -6; b = 22; c = 0;
Δ = b2-4ac
Δ = 222-4·(-6)·0
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-22}{2*-6}=\frac{-44}{-12}
=3+2/3
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+22}{2*-6}=\frac{0}{-12}
=0
$