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

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

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

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 6x+2)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


576x^2/216x^2+162x/216x^2+(-36x)/216x^2-2=0

We multiply all the terms by the denominator


576x^2+162x+(-36x)-2*216x^2=0

Wy multiply elements

576x^2-432x^2+162x+(-36x)=0

We get rid of parentheses

576x^2-432x^2+162x-36x=0

We add all the numbers together, and all the variables

144x^2+126x=0

a = 144; b = 126; c = 0;
Δ = b2-4ac
Δ = 1262-4·144·0
Δ = 15876
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{15876}=126$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(126)-126}{2*144}=\frac{-252}{288}
=-7/8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(126)+126}{2*144}=\frac{0}{288}
=0
$