8x+4/x-5=40+4/x-5

Solution for 8x+4/x-5=40+4/x-5 equation:

8x+4/x-5=40+4/x-5

We move all terms to the left:

8x+4/x-5-(40+4/x-5)=0


Domain of the equation: x!=0

x∈R



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

x∈R


We add all the numbers together, and all the variables

8x+4/x-(4/x+35)-5=0

We get rid of parentheses

8x+4/x-4/x-35-5=0

We multiply all the terms by the denominator


8x*x-35*x-5*x+4-4=0

We add all the numbers together, and all the variables

-40x+8x*x=0

Wy multiply elements

8x^2-40x=0

a = 8; b = -40; c = 0;
Δ = b2-4ac
Δ = -402-4·8·0
Δ = 1600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1600}=40$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-40}{2*8}=\frac{0}{16}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+40}{2*8}=\frac{80}{16}
=5
$