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

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



5/6x+2-x=1/6x
We move all terms to the left:
5/6x+2-x-(1/6x)=0
Domain of the equation: 6x!=0
x!=0/6
x!=0
x∈R
Domain of the equation: 6x)!=0
x!=0/1
x!=0
x∈R
We add all the numbers together, and all the variables
5/6x-x-(+1/6x)+2=0
We add all the numbers together, and all the variables
-1x+5/6x-(+1/6x)+2=0
We get rid of parentheses
-1x+5/6x-1/6x+2=0
We multiply all the terms by the denominator
-1x*6x+2*6x+5-1=0
We add all the numbers together, and all the variables
-1x*6x+2*6x+4=0
Wy multiply elements
-6x^2+12x+4=0
a = -6; b = 12; c = +4;
Δ = b2-4ac
Δ = 122-4·(-6)·4
Δ = 240
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:
$\sqrt{\Delta}=\sqrt{240}=\sqrt{16*15}=\sqrt{16}*\sqrt{15}=4\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-4\sqrt{15}}{2*-6}=\frac{-12-4\sqrt{15}}{-12} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+4\sqrt{15}}{2*-6}=\frac{-12+4\sqrt{15}}{-12} $

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