1/u-1/2.5u=1/5.

Solution for 1/u-1/2.5u=1/5. equation:

1/u-1/2.5u=1/5.

We move all terms to the left:

1/u-1/2.5u-(1/5.)=0


Domain of the equation: u!=0

u∈R



Domain of the equation: 2.5u!=0

u!=0/2.5

u!=0

u∈R


We add all the numbers together, and all the variables

1/u-1/2.5u-(+1/5.)=0

We get rid of parentheses

1/u-1/2.5u-1/5.=0

We calculate fractions


(-4u^2)/10u^2+10u/10u^2+(-25u)/10u^2=0

We multiply all the terms by the denominator


(-4u^2)+10u+(-25u)=0

We get rid of parentheses

-4u^2+10u-25u=0

We add all the numbers together, and all the variables

-4u^2-15u=0

a = -4; b = -15; c = 0;
Δ = b2-4ac
Δ = -152-4·(-4)·0
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-15}{2*-4}=\frac{0}{-8}
=0
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+15}{2*-4}=\frac{30}{-8}
=-3+3/4
$