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3+1/3x+4/6x=14
We move all terms to the left:
3+1/3x+4/6x-(14)=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!=0/6
x!=0
x∈R
1/3x+4/6x-11=0
We calculate fractions
6x/18x^2+12x/18x^2-11=0
We multiply all the terms by the denominator
6x+12x-11*18x^2=0
We add all the numbers together, and all the variables
18x-11*18x^2=0
Wy multiply elements
-198x^2+18x=0
a = -198; b = 18; c = 0;
Δ = b2-4ac
Δ = 182-4·(-198)·0
Δ = 324
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{324}=18$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-18}{2*-198}=\frac{-36}{-396} =1/11 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+18}{2*-198}=\frac{0}{-396} =0 $
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