4(3-u)/u=22+2u

Solution for 4(3-u)/u=22+2u equation:

4(3-u)/u=22+2u

We move all terms to the left:

4(3-u)/u-(22+2u)=0


Domain of the equation: u!=0

u∈R


We add all the numbers together, and all the variables

4(-1u+3)/u-(2u+22)=0

We get rid of parentheses

4(-1u+3)/u-2u-22=0

We multiply all the terms by the denominator


4(-1u+3)-2u*u-22*u=0

We add all the numbers together, and all the variables

-22u+4(-1u+3)-2u*u=0

We multiply parentheses

-22u-4u-2u*u+12=0

Wy multiply elements

-2u^2-22u-4u+12=0

We add all the numbers together, and all the variables

-2u^2-26u+12=0

a = -2; b = -26; c = +12;
Δ = b2-4ac
Δ = -262-4·(-2)·12
Δ = 772
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:

$\sqrt{\Delta}=\sqrt{772}=\sqrt{4*193}=\sqrt{4}*\sqrt{193}=2\sqrt{193}$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-26)-2\sqrt{193}}{2*-2}=\frac{26-2\sqrt{193}}{-4}
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-26)+2\sqrt{193}}{2*-2}=\frac{26+2\sqrt{193}}{-4}
$