5/u=16-3u

Solution for 5/u=16-3u equation:

5/u=16-3u

We move all terms to the left:

5/u-(16-3u)=0


Domain of the equation: u!=0

u∈R


We add all the numbers together, and all the variables

5/u-(-3u+16)=0

We get rid of parentheses

5/u+3u-16=0

We multiply all the terms by the denominator


3u*u-16*u+5=0

We add all the numbers together, and all the variables

-16u+3u*u+5=0

Wy multiply elements

3u^2-16u+5=0

a = 3; b = -16; c = +5;
Δ = b2-4ac
Δ = -162-4·3·5
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-14}{2*3}=\frac{2}{6}
=1/3
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+14}{2*3}=\frac{30}{6}
=5
$