u+1/u=5

Solution for u+1/u=5 equation:

u+1/u=5

We move all terms to the left:

u+1/u-(5)=0


Domain of the equation: u!=0

u∈R


We multiply all the terms by the denominator


u*u-5*u+1=0

We add all the numbers together, and all the variables

-5u+u*u+1=0

Wy multiply elements

u^2-5u+1=0

a = 1; b = -5; c = +1;
Δ = b2-4ac
Δ = -52-4·1·1
Δ = 21
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-\sqrt{21}}{2*1}=\frac{5-\sqrt{21}}{2}
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{21}}{2*1}=\frac{5+\sqrt{21}}{2}
$