X+28/x=11

Solution for X+28/x=11 equation:

X+28/X=11

We move all terms to the left:

X+28/X-(11)=0


Domain of the equation: X!=0

X∈R


We multiply all the terms by the denominator


X*X-11*X+28=0

We add all the numbers together, and all the variables

-11X+X*X+28=0

Wy multiply elements

X^2-11X+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:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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