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1/3x+4/81x=-31
We move all terms to the left:
1/3x+4/81x-(-31)=0
Domain of the equation: 3x!=0
x!=0/3
x!=0
x∈R
Domain of the equation: 81x!=0We add all the numbers together, and all the variables
x!=0/81
x!=0
x∈R
1/3x+4/81x+31=0
We calculate fractions
81x/243x^2+12x/243x^2+31=0
We multiply all the terms by the denominator
81x+12x+31*243x^2=0
We add all the numbers together, and all the variables
93x+31*243x^2=0
Wy multiply elements
7533x^2+93x=0
a = 7533; b = 93; c = 0;
Δ = b2-4ac
Δ = 932-4·7533·0
Δ = 8649
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{8649}=93$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(93)-93}{2*7533}=\frac{-186}{15066} =-1/81 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(93)+93}{2*7533}=\frac{0}{15066} =0 $
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