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40-2/3x=32-1/6x
We move all terms to the left:
40-2/3x-(32-1/6x)=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-(-1/6x+32)+40=0
We get rid of parentheses
-2/3x+1/6x-32+40=0
We calculate fractions
(-12x)/18x^2+3x/18x^2-32+40=0
We add all the numbers together, and all the variables
(-12x)/18x^2+3x/18x^2+8=0
We multiply all the terms by the denominator
(-12x)+3x+8*18x^2=0
We add all the numbers together, and all the variables
3x+(-12x)+8*18x^2=0
Wy multiply elements
144x^2+3x+(-12x)=0
We get rid of parentheses
144x^2+3x-12x=0
We add all the numbers together, and all the variables
144x^2-9x=0
a = 144; b = -9; c = 0;
Δ = b2-4ac
Δ = -92-4·144·0
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$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-9}{2*144}=\frac{0}{288} =0 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+9}{2*144}=\frac{18}{288} =1/16 $
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