F(x)=4x^2/x-16

Solution for F(x)=4x^2/x-16 equation:

(F)=4F^2/F-16

We move all terms to the left:

(F)-(4F^2/F-16)=0


Domain of the equation: F-16)!=0

F∈R


We get rid of parentheses

-4F^2/F+F+16=0

We multiply all the terms by the denominator


-4F^2+F*F+16*F=0

We add all the numbers together, and all the variables

-4F^2+16F+F*F=0

Wy multiply elements

-4F^2+F^2+16F=0

We add all the numbers together, and all the variables

-3F^2+16F=0

a = -3; b = 16; c = 0;
Δ = b2-4ac
Δ = 162-4·(-3)·0
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-16}{2*-3}=\frac{-32}{-6}
=5+1/3
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+16}{2*-3}=\frac{0}{-6}
=0
$