x=4x*1/x^-5*x^-3

Solution for x=4x*1/x^-5*x^-3 equation:

x=4x*1/x^-5x^-3

We move all terms to the left:

x-(4x*1/x^-5x^-3)=0


Domain of the equation: x^-5x^-3)!=0

x∈R


We get rid of parentheses

x-4x*1/x^+5x^+3=0

We multiply all the terms by the denominator


x*x^-4x*1+5x^*x^+3*x^=0

We add all the numbers together, and all the variables

3x+x*x^-4x*1+5x^*x^=0

Wy multiply elements

x^2+5x^2+3x-4x=0

We add all the numbers together, and all the variables

6x^2-1x=0

a = 6; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·6·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-1}{2*6}=\frac{0}{12}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*6}=\frac{2}{12}
=1/6
$