4/x+3x=14

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}
$