-3/2u-4+4=6/u-2

Solution for -3/2u-4+4=6/u-2 equation:

-3/2u-4+4=6/u-2

We move all terms to the left:

-3/2u-4+4-(6/u-2)=0


Domain of the equation: 2u!=0

u!=0/2

u!=0

u∈R



Domain of the equation: u-2)!=0

u∈R


We add all the numbers together, and all the variables

-3/2u-(6/u-2)=0

We get rid of parentheses

-3/2u-6/u+2=0

We calculate fractions


(-3u)/2u^2+(-12u)/2u^2+2=0

We multiply all the terms by the denominator


(-3u)+(-12u)+2*2u^2=0

Wy multiply elements

4u^2+(-3u)+(-12u)=0

We get rid of parentheses

4u^2-3u-12u=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
$