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

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

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

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



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

x∈R


We get rid of parentheses

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

We calculate fractions


(-324x^2)/288x^2+192x/288x^2+(-48x)/288x^2-2=0

We multiply all the terms by the denominator


(-324x^2)+192x+(-48x)-2*288x^2=0

Wy multiply elements

(-324x^2)-576x^2+192x+(-48x)=0

We get rid of parentheses

-324x^2-576x^2+192x-48x=0

We add all the numbers together, and all the variables

-900x^2+144x=0

a = -900; b = 144; c = 0;
Δ = b2-4ac
Δ = 1442-4·(-900)·0
Δ = 20736
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{20736}=144$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(144)-144}{2*-900}=\frac{-288}{-1800}
=4/25
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(144)+144}{2*-900}=\frac{0}{-1800}
=0
$