2/3x+1/6x=2

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



2/3x+1/6x=2
We move all terms to the left:
2/3x+1/6x-(2)=0
Domain of the equation: 3x!=0
x!=0/3
x!=0
x∈R
Domain of the equation: 6x!=0
x!=0/6
x!=0
x∈R
We calculate fractions
12x/18x^2+3x/18x^2-2=0
We multiply all the terms by the denominator
12x+3x-2*18x^2=0
We add all the numbers together, and all the variables
15x-2*18x^2=0
Wy multiply elements
-36x^2+15x=0
a = -36; b = 15; c = 0;
Δ = b2-4ac
Δ = 152-4·(-36)·0
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-15}{2*-36}=\frac{-30}{-72} =5/12 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+15}{2*-36}=\frac{0}{-72} =0 $

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