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4x+1/3x=11
We move all terms to the left:
4x+1/3x-(11)=0
Domain of the equation: 3x!=0We multiply all the terms by the denominator
x!=0/3
x!=0
x∈R
4x*3x-11*3x+1=0
Wy multiply elements
12x^2-33x+1=0
a = 12; b = -33; c = +1;
Δ = b2-4ac
Δ = -332-4·12·1
Δ = 1041
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{-(-33)-\sqrt{1041}}{2*12}=\frac{33-\sqrt{1041}}{24} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-33)+\sqrt{1041}}{2*12}=\frac{33+\sqrt{1041}}{24} $
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