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

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

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

We move all terms to the left:

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


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R



Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


40x/48x^2+(-6x)/48x^2+6x/48x^2-2=0

We multiply all the terms by the denominator


40x+(-6x)+6x-2*48x^2=0

We add all the numbers together, and all the variables

46x+(-6x)-2*48x^2=0

Wy multiply elements

-96x^2+46x+(-6x)=0

We get rid of parentheses

-96x^2+46x-6x=0

We add all the numbers together, and all the variables

-96x^2+40x=0

a = -96; b = 40; c = 0;
Δ = b2-4ac
Δ = 402-4·(-96)·0
Δ = 1600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1600}=40$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-40}{2*-96}=\frac{-80}{-192}
=5/12
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+40}{2*-96}=\frac{0}{-192}
=0
$