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2x-1/(3x)=5
We move all terms to the left:
2x-1/(3x)-(5)=0
Domain of the equation: 3x!=0We multiply all the terms by the denominator
x!=0/3
x!=0
x∈R
2x*3x-5*3x-1=0
Wy multiply elements
6x^2-15x-1=0
a = 6; b = -15; c = -1;
Δ = b2-4ac
Δ = -152-4·6·(-1)
Δ = 249
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{-(-15)-\sqrt{249}}{2*6}=\frac{15-\sqrt{249}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+\sqrt{249}}{2*6}=\frac{15+\sqrt{249}}{12} $
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