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

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

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

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


(-648x^2)/576x^2+(-576x^2)/576x^2+288x/576x^2+(-96x)/576x^2=0

We multiply all the terms by the denominator


(-648x^2)+(-576x^2)+288x+(-96x)=0

We get rid of parentheses

-648x^2-576x^2+288x-96x=0

We add all the numbers together, and all the variables

-1224x^2+192x=0

a = -1224; b = 192; c = 0;
Δ = b2-4ac
Δ = 1922-4·(-1224)·0
Δ = 36864
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36864}=192$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(192)-192}{2*-1224}=\frac{-384}{-2448}
=8/51
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(192)+192}{2*-1224}=\frac{0}{-2448}
=0
$