6/u-1=9/2u

Solution for 6/u-1=9/2u equation:

6/u-1=9/2u

We move all terms to the left:

6/u-1-(9/2u)=0


Domain of the equation: u!=0

u∈R



Domain of the equation: 2u)!=0

u!=0/1

u!=0

u∈R


We add all the numbers together, and all the variables

6/u-(+9/2u)-1=0

We get rid of parentheses

6/u-9/2u-1=0

We calculate fractions


12u/2u^2+(-9u)/2u^2-1=0

We multiply all the terms by the denominator


12u+(-9u)-1*2u^2=0

Wy multiply elements

-2u^2+12u+(-9u)=0

We get rid of parentheses

-2u^2+12u-9u=0

We add all the numbers together, and all the variables

-2u^2+3u=0

a = -2; b = 3; c = 0;
Δ = b2-4ac
Δ = 32-4·(-2)·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3}{2*-2}=\frac{-6}{-4}
=1+1/2
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3}{2*-2}=\frac{0}{-4}
=0
$