F(x)=3/x-14

Solution for F(x)=3/x-14 equation:

(F)=3/F-14

We move all terms to the left:

(F)-(3/F-14)=0


Domain of the equation: F-14)!=0

F∈R


We get rid of parentheses

F-3/F+14=0

We multiply all the terms by the denominator


F*F+14*F-3=0

We add all the numbers together, and all the variables

14F+F*F-3=0

Wy multiply elements

F^2+14F-3=0

a = 1; b = 14; c = -3;
Δ = b2-4ac
Δ = 142-4·1·(-3)
Δ = 208
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:

$\sqrt{\Delta}=\sqrt{208}=\sqrt{16*13}=\sqrt{16}*\sqrt{13}=4\sqrt{13}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-4\sqrt{13}}{2*1}=\frac{-14-4\sqrt{13}}{2}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+4\sqrt{13}}{2*1}=\frac{-14+4\sqrt{13}}{2}
$