5/u-5=-1/4u-20+1

Solution for 5/u-5=-1/4u-20+1 equation:

5/u-5=-1/4u-20+1

We move all terms to the left:

5/u-5-(-1/4u-20+1)=0


Domain of the equation: u!=0

u∈R



Domain of the equation: 4u-20+1)!=0

We move all terms containing u to the left, all other terms to the right

4u+1)!=20

u∈R


We add all the numbers together, and all the variables

5/u-(-1/4u-19)-5=0

We get rid of parentheses

5/u+1/4u+19-5=0

We calculate fractions


20u/4u^2+u/4u^2+19-5=0

We add all the numbers together, and all the variables

20u/4u^2+u/4u^2+14=0

We multiply all the terms by the denominator


20u+u+14*4u^2=0

We add all the numbers together, and all the variables

21u+14*4u^2=0

Wy multiply elements

56u^2+21u=0

a = 56; b = 21; c = 0;
Δ = b2-4ac
Δ = 212-4·56·0
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-21}{2*56}=\frac{-42}{112}
=-3/8
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+21}{2*56}=\frac{0}{112}
=0
$