5/2u+4=-3/u+2

Solution for 5/2u+4=-3/u+2 equation:

5/2u+4=-3/u+2

We move all terms to the left:

5/2u+4-(-3/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 get rid of parentheses

5/2u+3/u-2+4=0

We calculate fractions


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

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

11u+2*2u^2=0

Wy multiply elements

4u^2+11u=0

a = 4; b = 11; c = 0;
Δ = b2-4ac
Δ = 112-4·4·0
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-11}{2*4}=\frac{-22}{8}
=-2+3/4
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+11}{2*4}=\frac{0}{8}
=0
$