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6x+1/3x=5
We move all terms to the left:
6x+1/3x-(5)=0
Domain of the equation: 3x!=0We multiply all the terms by the denominator
x!=0/3
x!=0
x∈R
6x*3x-5*3x+1=0
Wy multiply elements
18x^2-15x+1=0
a = 18; b = -15; c = +1;
Δ = b2-4ac
Δ = -152-4·18·1
Δ = 153
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{153}=\sqrt{9*17}=\sqrt{9}*\sqrt{17}=3\sqrt{17}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-3\sqrt{17}}{2*18}=\frac{15-3\sqrt{17}}{36} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+3\sqrt{17}}{2*18}=\frac{15+3\sqrt{17}}{36} $
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