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5/9x+2=1/6x=11/18x+1/3
We move all terms to the left:
5/9x+2-(1/6x)=0
Domain of the equation: 9x!=0
x!=0/9
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
5/9x-(+1/6x)+2=0
We get rid of parentheses
5/9x-1/6x+2=0
We calculate fractions
30x/54x^2+(-9x)/54x^2+2=0
We multiply all the terms by the denominator
30x+(-9x)+2*54x^2=0
Wy multiply elements
108x^2+30x+(-9x)=0
We get rid of parentheses
108x^2+30x-9x=0
We add all the numbers together, and all the variables
108x^2+21x=0
a = 108; b = 21; c = 0;
Δ = b2-4ac
Δ = 212-4·108·0
Δ = 441
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{441}=21$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-21}{2*108}=\frac{-42}{216} =-7/36 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+21}{2*108}=\frac{0}{216} =0 $
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