3/u-4=-6/5u-20+1

Solution for 3/u-4=-6/5u-20+1 equation:

3/u-4=-6/5u-20+1

We move all terms to the left:

3/u-4-(-6/5u-20+1)=0


Domain of the equation: u!=0

u∈R



Domain of the equation: 5u-20+1)!=0

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

5u+1)!=20

u∈R


We add all the numbers together, and all the variables

3/u-(-6/5u-19)-4=0

We get rid of parentheses

3/u+6/5u+19-4=0

We calculate fractions


15u/5u^2+6u/5u^2+19-4=0

We add all the numbers together, and all the variables

15u/5u^2+6u/5u^2+15=0

We multiply all the terms by the denominator


15u+6u+15*5u^2=0

We add all the numbers together, and all the variables

21u+15*5u^2=0

Wy multiply elements

75u^2+21u=0

a = 75; b = 21; c = 0;
Δ = b2-4ac
Δ = 212-4·75·0
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*75}=\frac{-42}{150}
=-7/25
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+21}{2*75}=\frac{0}{150}
=0
$