5x=4x+6+16/x

Solution for 5x=4x+6+16/x equation:

5x=4x+6+16/x

We move all terms to the left:

5x-(4x+6+16/x)=0


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

5x-(4x+16/x+6)=0

We get rid of parentheses

5x-4x-16/x-6=0

We multiply all the terms by the denominator


5x*x-4x*x-6*x-16=0

We add all the numbers together, and all the variables

-6x+5x*x-4x*x-16=0

Wy multiply elements

5x^2-4x^2-6x-16=0

We add all the numbers together, and all the variables

x^2-6x-16=0

a = 1; b = -6; c = -16;
Δ = b2-4ac
Δ = -62-4·1·(-16)
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-10}{2*1}=\frac{-4}{2}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+10}{2*1}=\frac{16}{2}
=8
$