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2x-1/3x=55
We move all terms to the left:
2x-1/3x-(55)=0
Domain of the equation: 3x!=0We multiply all the terms by the denominator
x!=0/3
x!=0
x∈R
2x*3x-55*3x-1=0
Wy multiply elements
6x^2-165x-1=0
a = 6; b = -165; c = -1;
Δ = b2-4ac
Δ = -1652-4·6·(-1)
Δ = 27249
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{-(-165)-\sqrt{27249}}{2*6}=\frac{165-\sqrt{27249}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-165)+\sqrt{27249}}{2*6}=\frac{165+\sqrt{27249}}{12} $
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