-1/u-5=2/5u-25

Solution for -1/u-5=2/5u-25 equation:

-1/u-5=2/5u-25

We move all terms to the left:

-1/u-5-(2/5u-25)=0


Domain of the equation: u!=0

u∈R



Domain of the equation: 5u-25)!=0

u∈R


We get rid of parentheses

-1/u-2/5u+25-5=0

We calculate fractions


(-5u)/5u^2+(-2u)/5u^2+25-5=0

We add all the numbers together, and all the variables

(-5u)/5u^2+(-2u)/5u^2+20=0

We multiply all the terms by the denominator


(-5u)+(-2u)+20*5u^2=0

Wy multiply elements

100u^2+(-5u)+(-2u)=0

We get rid of parentheses

100u^2-5u-2u=0

We add all the numbers together, and all the variables

100u^2-7u=0

a = 100; b = -7; c = 0;
Δ = b2-4ac
Δ = -72-4·100·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-7}{2*100}=\frac{0}{200}
=0
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+7}{2*100}=\frac{14}{200}
=7/100
$