(-)3/u+6=-5/2u+12+4

Solution for (-)3/u+6=-5/2u+12+4 equation:

(-)3/u+6=-5/2u+12+4

We move all terms to the left:

(-)3/u+6-(-5/2u+12+4)=0


Domain of the equation: u!=0

u∈R



Domain of the equation: 2u+12+4)!=0

We move all terms containing u to the left, all other terms to the right

2u+4)!=-12

u∈R


We add all the numbers together, and all the variables

03/u-(-5/2u+16)+6=0

We get rid of parentheses

03/u+5/2u-16+6=0

We calculate fractions


6u/2u^2+5u/2u^2-16+6=0

We add all the numbers together, and all the variables

6u/2u^2+5u/2u^2-10=0

We multiply all the terms by the denominator


6u+5u-10*2u^2=0

We add all the numbers together, and all the variables

11u-10*2u^2=0

Wy multiply elements

-20u^2+11u=0

a = -20; b = 11; c = 0;
Δ = b2-4ac
Δ = 112-4·(-20)·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*-20}=\frac{-22}{-40}
=11/20
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+11}{2*-20}=\frac{0}{-40}
=0
$