-11=u+28/u

Solution for -11=u+28/u equation:

-11=u+28/u

We move all terms to the left:

-11-(u+28/u)=0


Domain of the equation: u)!=0

u!=0/1

u!=0

u∈R


We add all the numbers together, and all the variables

-(+u+28/u)-11=0

We get rid of parentheses

-u-28/u-11=0

We multiply all the terms by the denominator


-u*u-11*u-28=0

We add all the numbers together, and all the variables

-11u-u*u-28=0

Wy multiply elements

-1u^2-11u-28=0

a = -1; b = -11; c = -28;
Δ = b2-4ac
Δ = -112-4·(-1)·(-28)
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-3}{2*-1}=\frac{8}{-2}
=-4
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+3}{2*-1}=\frac{14}{-2}
=-7
$