4/x+3x=14

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Solution for 4/x+3x=14 equation:



4/x+3x=14
We move all terms to the left:
4/x+3x-(14)=0
Domain of the equation: x!=0
x∈R
We add all the numbers together, and all the variables
3x+4/x-14=0
We multiply all the terms by the denominator
3x*x-14*x+4=0
We add all the numbers together, and all the variables
-14x+3x*x+4=0
Wy multiply elements
3x^2-14x+4=0
a = 3; b = -14; c = +4;
Δ = b2-4ac
Δ = -142-4·3·4
Δ = 148
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:
$\sqrt{\Delta}=\sqrt{148}=\sqrt{4*37}=\sqrt{4}*\sqrt{37}=2\sqrt{37}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{37}}{2*3}=\frac{14-2\sqrt{37}}{6} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{37}}{2*3}=\frac{14+2\sqrt{37}}{6} $

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