-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

-3/u-(-5/2u+16)+6=0

We get rid of parentheses

-3/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

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

Wy multiply elements

-20u^2+5u+(-6u)=0

We get rid of parentheses

-20u^2+5u-6u=0

We add all the numbers together, and all the variables

-20u^2-1u=0

a = -20; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·(-20)·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-1}{2*-20}=\frac{0}{-40}
=0
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*-20}=\frac{2}{-40}
=-1/20
$