15x^-1/3x^-3=0

Solution for 15x^-1/3x^-3=0 equation:

15x^-1/3x^-3=0


Domain of the equation: 3x^!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

15x-1/3x^-3=0

We multiply all the terms by the denominator


15x*3x^-3*3x^-1=0

Wy multiply elements

45x^2-9x-1=0

a = 45; b = -9; c = -1;
Δ = b2-4ac
Δ = -92-4·45·(-1)
Δ = 261
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{261}=\sqrt{9*29}=\sqrt{9}*\sqrt{29}=3\sqrt{29}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-3\sqrt{29}}{2*45}=\frac{9-3\sqrt{29}}{90}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+3\sqrt{29}}{2*45}=\frac{9+3\sqrt{29}}{90}
$