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x+1/3x=84
We move all terms to the left:
x+1/3x-(84)=0
Domain of the equation: 3x!=0We multiply all the terms by the denominator
x!=0/3
x!=0
x∈R
x*3x-84*3x+1=0
Wy multiply elements
3x^2-252x+1=0
a = 3; b = -252; c = +1;
Δ = b2-4ac
Δ = -2522-4·3·1
Δ = 63492
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{63492}=\sqrt{4*15873}=\sqrt{4}*\sqrt{15873}=2\sqrt{15873}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-252)-2\sqrt{15873}}{2*3}=\frac{252-2\sqrt{15873}}{6} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-252)+2\sqrt{15873}}{2*3}=\frac{252+2\sqrt{15873}}{6} $
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