F(x)=16x-8/x

Solution for F(x)=16x-8/x equation:

(F)=16F-8/F

We move all terms to the left:

(F)-(16F-8/F)=0


Domain of the equation: F)!=0

F!=0/1

F!=0

F∈R


We add all the numbers together, and all the variables

F-(+16F-8/F)=0

We get rid of parentheses

F-16F+8/F=0

We multiply all the terms by the denominator


F*F-16F*F+8=0

Wy multiply elements

F^2-16F^2+8=0

We add all the numbers together, and all the variables

-15F^2+8=0

a = -15; b = 0; c = +8;
Δ = b2-4ac
Δ = 02-4·(-15)·8
Δ = 480
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:

$\sqrt{\Delta}=\sqrt{480}=\sqrt{16*30}=\sqrt{16}*\sqrt{30}=4\sqrt{30}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{30}}{2*-15}=\frac{0-4\sqrt{30}}{-30}
=-\frac{4\sqrt{30}}{-30}
=-\frac{2\sqrt{30}}{-15}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{30}}{2*-15}=\frac{0+4\sqrt{30}}{-30}
=\frac{4\sqrt{30}}{-30}
=\frac{2\sqrt{30}}{-15}
$