3x^-4-2x^-3-1/x^-2=0

Solution for 3x^-4-2x^-3-1/x^-2=0 equation:

3x^-4-2x^-3-1/x^-2=0


Domain of the equation: x^!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

x-1/x^-9=0

We multiply all the terms by the denominator


x*x^-9*x^-1=0

We add all the numbers together, and all the variables

-9x+x*x^-1=0

Wy multiply elements

x^2-9x-1=0

a = 1; b = -9; c = -1;
Δ = b2-4ac
Δ = -92-4·1·(-1)
Δ = 85
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{-(-9)-\sqrt{85}}{2*1}=\frac{9-\sqrt{85}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{85}}{2*1}=\frac{9+\sqrt{85}}{2}
$