F(x)=1/5x^-3

Solution for F(x)=1/5x^-3 equation:

(F)=1/5F^-3

We move all terms to the left:

(F)-(1/5F^-3)=0


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

F∈R


We get rid of parentheses

F-1/5F^+3=0

We multiply all the terms by the denominator


F*5F^+3*5F^-1=0

Wy multiply elements

5F^2+15F-1=0

a = 5; b = 15; c = -1;
Δ = b2-4ac
Δ = 152-4·5·(-1)
Δ = 245
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{245}=\sqrt{49*5}=\sqrt{49}*\sqrt{5}=7\sqrt{5}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-7\sqrt{5}}{2*5}=\frac{-15-7\sqrt{5}}{10}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+7\sqrt{5}}{2*5}=\frac{-15+7\sqrt{5}}{10}
$