2x+14/x=16

Solution for 2x+14/x=16 equation:

2x+14/x=16

We move all terms to the left:

2x+14/x-(16)=0


Domain of the equation: x!=0

x∈R


We multiply all the terms by the denominator


2x*x-16*x+14=0

We add all the numbers together, and all the variables

-16x+2x*x+14=0

Wy multiply elements

2x^2-16x+14=0

a = 2; b = -16; c = +14;
Δ = b2-4ac
Δ = -162-4·2·14
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-12}{2*2}=\frac{4}{4}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+12}{2*2}=\frac{28}{4}
=7
$