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

Solution for 1/6x-3+3/2x-1-2/3=0 equation:

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


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R



Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

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

We calculate fractions


(-48x^2)/108x^2+18x/108x^2+162x/108x^2-4=0

We multiply all the terms by the denominator


(-48x^2)+18x+162x-4*108x^2=0

We add all the numbers together, and all the variables

(-48x^2)+180x-4*108x^2=0

Wy multiply elements

(-48x^2)-432x^2+180x=0

We get rid of parentheses

-48x^2-432x^2+180x=0

We add all the numbers together, and all the variables

-480x^2+180x=0

a = -480; b = 180; c = 0;
Δ = b2-4ac
Δ = 1802-4·(-480)·0
Δ = 32400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{32400}=180$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(180)-180}{2*-480}=\frac{-360}{-960}
=3/8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(180)+180}{2*-480}=\frac{0}{-960}
=0
$