F(x)=7x-4/x+3

Solution for F(x)=7x-4/x+3 equation:

(F)=7F-4/F+3

We move all terms to the left:

(F)-(7F-4/F+3)=0


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

F∈R


We get rid of parentheses

F-7F+4/F-3=0

We multiply all the terms by the denominator


F*F-7F*F-3*F+4=0

We add all the numbers together, and all the variables

-3F+F*F-7F*F+4=0

Wy multiply elements

F^2-7F^2-3F+4=0

We add all the numbers together, and all the variables

-6F^2-3F+4=0

a = -6; b = -3; c = +4;
Δ = b2-4ac
Δ = -32-4·(-6)·4
Δ = 105
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{105}}{2*-6}=\frac{3-\sqrt{105}}{-12}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{105}}{2*-6}=\frac{3+\sqrt{105}}{-12}
$