3x+21/x=16

Solution for 3x+21/x=16 equation:

3x+21/x=16

We move all terms to the left:

3x+21/x-(16)=0


Domain of the equation: x!=0

x∈R


We multiply all the terms by the denominator


3x*x-16*x+21=0

We add all the numbers together, and all the variables

-16x+3x*x+21=0

Wy multiply elements

3x^2-16x+21=0

a = 3; b = -16; c = +21;
Δ = b2-4ac
Δ = -162-4·3·21
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-2}{2*3}=\frac{14}{6}
=2+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+2}{2*3}=\frac{18}{6}
=3
$