1/6x+4/3=1/2x-1

Solution for 1/6x+4/3=1/2x-1 equation:

1/6x+4/3=1/2x-1

We move all terms to the left:

1/6x+4/3-(1/2x-1)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R



Domain of the equation: 2x-1)!=0

x∈R


We get rid of parentheses

1/6x-1/2x+1+4/3=0

We calculate fractions


96x^2/108x^2+18x/108x^2+(-54x)/108x^2+1=0

We multiply all the terms by the denominator


96x^2+18x+(-54x)+1*108x^2=0

Wy multiply elements

96x^2+108x^2+18x+(-54x)=0

We get rid of parentheses

96x^2+108x^2+18x-54x=0

We add all the numbers together, and all the variables

204x^2-36x=0

a = 204; b = -36; c = 0;
Δ = b2-4ac
Δ = -362-4·204·0
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-36}{2*204}=\frac{0}{408}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+36}{2*204}=\frac{72}{408}
=3/17
$