1/u+1/4u=1

Solution for 1/u+1/4u=1 equation:

1/u+1/4u=1

We move all terms to the left:

1/u+1/4u-(1)=0


Domain of the equation: u!=0

u∈R



Domain of the equation: 4u!=0

u!=0/4

u!=0

u∈R


We calculate fractions


4u/4u^2+u/4u^2-1=0

We multiply all the terms by the denominator


4u+u-1*4u^2=0

We add all the numbers together, and all the variables

5u-1*4u^2=0

Wy multiply elements

-4u^2+5u=0

a = -4; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·(-4)·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5}{2*-4}=\frac{-10}{-8}
=1+1/4
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*-4}=\frac{0}{-8}
=0
$