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3x-1/x+7=0
Domain of the equation: x!=0We multiply all the terms by the denominator
x∈R
3x*x+7*x-1=0
We add all the numbers together, and all the variables
7x+3x*x-1=0
Wy multiply elements
3x^2+7x-1=0
a = 3; b = 7; c = -1;
Δ = b2-4ac
Δ = 72-4·3·(-1)
Δ = 61
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-\sqrt{61}}{2*3}=\frac{-7-\sqrt{61}}{6} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{61}}{2*3}=\frac{-7+\sqrt{61}}{6} $
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