2u+2=4/u-4

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

2u+2=4/u-4

We move all terms to the left:

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


Domain of the equation: u-4)!=0

u∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


2u*u+4*u+2*u-4=0

We add all the numbers together, and all the variables

6u+2u*u-4=0

Wy multiply elements

2u^2+6u-4=0

a = 2; b = 6; c = -4;
Δ = b2-4ac
Δ = 62-4·2·(-4)
Δ = 68
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{68}=\sqrt{4*17}=\sqrt{4}*\sqrt{17}=2\sqrt{17}$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{17}}{2*2}=\frac{-6-2\sqrt{17}}{4}
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{17}}{2*2}=\frac{-6+2\sqrt{17}}{4}
$