5u=6-1/u

Solution for 5u=6-1/u equation:

5u=6-1/u

We move all terms to the left:

5u-(6-1/u)=0


Domain of the equation: u)!=0

u!=0/1

u!=0

u∈R


We add all the numbers together, and all the variables

5u-(-1/u+6)=0

We get rid of parentheses

5u+1/u-6=0

We multiply all the terms by the denominator


5u*u-6*u+1=0

We add all the numbers together, and all the variables

-6u+5u*u+1=0

Wy multiply elements

5u^2-6u+1=0

a = 5; b = -6; c = +1;
Δ = b2-4ac
Δ = -62-4·5·1
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-4}{2*5}=\frac{2}{10}
=1/5
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+4}{2*5}=\frac{10}{10}
=1
$