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1/6x+9/x*3+8=0
Domain of the equation: 6x!=0
x!=0/6
x!=0
x∈R
Domain of the equation: x*3!=0We calculate fractions
x!=0/1
x!=0
x∈R
9x/54x^2+54x/54x^2+8=0
We multiply all the terms by the denominator
9x+54x+8*54x^2=0
We add all the numbers together, and all the variables
63x+8*54x^2=0
Wy multiply elements
432x^2+63x=0
a = 432; b = 63; c = 0;
Δ = b2-4ac
Δ = 632-4·432·0
Δ = 3969
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{3969}=63$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(63)-63}{2*432}=\frac{-126}{864} =-7/48 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(63)+63}{2*432}=\frac{0}{864} =0 $
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