x+11/5x=384

Solution for x+11/5x=384 equation:

x+11/5x=384

We move all terms to the left:

x+11/5x-(384)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We multiply all the terms by the denominator


x*5x-384*5x+11=0

Wy multiply elements

5x^2-1920x+11=0

a = 5; b = -1920; c = +11;
Δ = b2-4ac
Δ = -19202-4·5·11
Δ = 3686180
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{3686180}=\sqrt{4*921545}=\sqrt{4}*\sqrt{921545}=2\sqrt{921545}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1920)-2\sqrt{921545}}{2*5}=\frac{1920-2\sqrt{921545}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1920)+2\sqrt{921545}}{2*5}=\frac{1920+2\sqrt{921545}}{10}
$