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1/6x+6=1/2x
We move all terms to the left:
1/6x+6-(1/2x)=0
Domain of the equation: 6x!=0
x!=0/6
x!=0
x∈R
Domain of the equation: 2x)!=0We add all the numbers together, and all the variables
x!=0/1
x!=0
x∈R
1/6x-(+1/2x)+6=0
We get rid of parentheses
1/6x-1/2x+6=0
We calculate fractions
2x/12x^2+(-6x)/12x^2+6=0
We multiply all the terms by the denominator
2x+(-6x)+6*12x^2=0
Wy multiply elements
72x^2+2x+(-6x)=0
We get rid of parentheses
72x^2+2x-6x=0
We add all the numbers together, and all the variables
72x^2-4x=0
a = 72; b = -4; c = 0;
Δ = b2-4ac
Δ = -42-4·72·0
Δ = 16
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{16}=4$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4}{2*72}=\frac{0}{144} =0 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4}{2*72}=\frac{8}{144} =1/18 $
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