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5x-1/3x=6
We move all terms to the left:
5x-1/3x-(6)=0
Domain of the equation: 3x!=0We multiply all the terms by the denominator
x!=0/3
x!=0
x∈R
5x*3x-6*3x-1=0
Wy multiply elements
15x^2-18x-1=0
a = 15; b = -18; c = -1;
Δ = b2-4ac
Δ = -182-4·15·(-1)
Δ = 384
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{384}=\sqrt{64*6}=\sqrt{64}*\sqrt{6}=8\sqrt{6}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-8\sqrt{6}}{2*15}=\frac{18-8\sqrt{6}}{30} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+8\sqrt{6}}{2*15}=\frac{18+8\sqrt{6}}{30} $
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