4-5/6x=1/2x+2

Solution for 4-5/6x=1/2x+2 equation:

4-5/6x=1/2x+2

We move all terms to the left:

4-5/6x-(1/2x+2)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R



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

x∈R


We get rid of parentheses

-5/6x-1/2x-2+4=0

We calculate fractions


(-10x)/12x^2+(-6x)/12x^2-2+4=0

We add all the numbers together, and all the variables

(-10x)/12x^2+(-6x)/12x^2+2=0

We multiply all the terms by the denominator


(-10x)+(-6x)+2*12x^2=0

Wy multiply elements

24x^2+(-10x)+(-6x)=0

We get rid of parentheses

24x^2-10x-6x=0

We add all the numbers together, and all the variables

24x^2-16x=0

a = 24; b = -16; c = 0;
Δ = b2-4ac
Δ = -162-4·24·0
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-16}{2*24}=\frac{0}{48}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+16}{2*24}=\frac{32}{48}
=2/3
$