x+4x/x-4=16/x-5

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

x+4x/x-4=16/x-5

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



Domain of the equation: x-5)!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

5x+x*x-16=0

Wy multiply elements

x^2+5x-16=0

a = 1; b = 5; c = -16;
Δ = b2-4ac
Δ = 52-4·1·(-16)
Δ = 89
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-\sqrt{89}}{2*1}=\frac{-5-\sqrt{89}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{89}}{2*1}=\frac{-5+\sqrt{89}}{2}
$