F(x)=8x/x-3

Solution for F(x)=8x/x-3 equation:

(F)=8F/F-3

We move all terms to the left:

(F)-(8F/F-3)=0


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

F∈R


We get rid of parentheses

F-8F/F+3=0

We multiply all the terms by the denominator


F*F-8F+3*F=0

We add all the numbers together, and all the variables

-5F+F*F=0

Wy multiply elements

F^2-5F=0

a = 1; b = -5; c = 0;
Δ = b2-4ac
Δ = -52-4·1·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5}{2*1}=\frac{0}{2}
=0
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5}{2*1}=\frac{10}{2}
=5
$