x^-5-4x/x-3=0

Solution for x^-5-4x/x-3=0 equation:

x^-5-4x/x-3=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

x-4x/x-8=0

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

-12x+x*x=0

Wy multiply elements

x^2-12x=0

a = 1; b = -12; c = 0;
Δ = b2-4ac
Δ = -122-4·1·0
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{-(-12)-12}{2*1}=\frac{0}{2}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+12}{2*1}=\frac{24}{2}
=12
$