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5/9x+8=1/6x+1
We move all terms to the left:
5/9x+8-(1/6x+1)=0
Domain of the equation: 9x!=0
x!=0/9
x!=0
x∈R
Domain of the equation: 6x+1)!=0We get rid of parentheses
x∈R
5/9x-1/6x-1+8=0
We calculate fractions
30x/54x^2+(-9x)/54x^2-1+8=0
We add all the numbers together, and all the variables
30x/54x^2+(-9x)/54x^2+7=0
We multiply all the terms by the denominator
30x+(-9x)+7*54x^2=0
Wy multiply elements
378x^2+30x+(-9x)=0
We get rid of parentheses
378x^2+30x-9x=0
We add all the numbers together, and all the variables
378x^2+21x=0
a = 378; b = 21; c = 0;
Δ = b2-4ac
Δ = 212-4·378·0
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$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-21}{2*378}=\frac{-42}{756} =-1/18 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+21}{2*378}=\frac{0}{756} =0 $
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