2x+1/3x=7

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Solution for 2x+1/3x=7 equation:



2x+1/3x=7
We move all terms to the left:
2x+1/3x-(7)=0
Domain of the equation: 3x!=0
x!=0/3
x!=0
x∈R
We multiply all the terms by the denominator
2x*3x-7*3x+1=0
Wy multiply elements
6x^2-21x+1=0
a = 6; b = -21; c = +1;
Δ = b2-4ac
Δ = -212-4·6·1
Δ = 417
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{-(-21)-\sqrt{417}}{2*6}=\frac{21-\sqrt{417}}{12} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+\sqrt{417}}{2*6}=\frac{21+\sqrt{417}}{12} $

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