4x-8/x+5=1

Solution for 4x-8/x+5=1 equation:

4x-8/x+5=1

We move all terms to the left:

4x-8/x+5-(1)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

4x-8/x+4=0

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

4x+4x*x-8=0

Wy multiply elements

4x^2+4x-8=0

a = 4; b = 4; c = -8;
Δ = b2-4ac
Δ = 42-4·4·(-8)
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-12}{2*4}=\frac{-16}{8}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+12}{2*4}=\frac{8}{8}
=1
$