-5/6x-2/3x=2

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Solution for -5/6x-2/3x=2 equation:



-5/6x-2/3x=2
We move all terms to the left:
-5/6x-2/3x-(2)=0
Domain of the equation: 6x!=0
x!=0/6
x!=0
x∈R
Domain of the equation: 3x!=0
x!=0/3
x!=0
x∈R
We calculate fractions
(-15x)/18x^2+(-12x)/18x^2-2=0
We multiply all the terms by the denominator
(-15x)+(-12x)-2*18x^2=0
Wy multiply elements
-36x^2+(-15x)+(-12x)=0
We get rid of parentheses
-36x^2-15x-12x=0
We add all the numbers together, and all the variables
-36x^2-27x=0
a = -36; b = -27; c = 0;
Δ = b2-4ac
Δ = -272-4·(-36)·0
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-27}{2*-36}=\frac{0}{-72} =0 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+27}{2*-36}=\frac{54}{-72} =-3/4 $

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