F(x)=-4x+12/x-3

Solution for F(x)=-4x+12/x-3 equation:

(F)=-4F+12/F-3

We move all terms to the left:

(F)-(-4F+12/F-3)=0


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

F∈R


We get rid of parentheses

F+4F-12/F+3=0

We multiply all the terms by the denominator


F*F+4F*F+3*F-12=0

We add all the numbers together, and all the variables

3F+F*F+4F*F-12=0

Wy multiply elements

F^2+4F^2+3F-12=0

We add all the numbers together, and all the variables

5F^2+3F-12=0

a = 5; b = 3; c = -12;
Δ = b2-4ac
Δ = 32-4·5·(-12)
Δ = 249
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-\sqrt{249}}{2*5}=\frac{-3-\sqrt{249}}{10}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{249}}{2*5}=\frac{-3+\sqrt{249}}{10}
$