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2/3x+6=7/6x
We move all terms to the left:
2/3x+6-(7/6x)=0
Domain of the equation: 3x!=0
x!=0/3
x!=0
x∈R
Domain of the equation: 6x)!=0We add all the numbers together, and all the variables
x!=0/1
x!=0
x∈R
2/3x-(+7/6x)+6=0
We get rid of parentheses
2/3x-7/6x+6=0
We calculate fractions
12x/18x^2+(-21x)/18x^2+6=0
We multiply all the terms by the denominator
12x+(-21x)+6*18x^2=0
Wy multiply elements
108x^2+12x+(-21x)=0
We get rid of parentheses
108x^2+12x-21x=0
We add all the numbers together, and all the variables
108x^2-9x=0
a = 108; b = -9; c = 0;
Δ = b2-4ac
Δ = -92-4·108·0
Δ = 81
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{81}=9$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-9}{2*108}=\frac{0}{216} =0 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+9}{2*108}=\frac{18}{216} =1/12 $
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