F(x)=12/x-23

Solution for F(x)=12/x-23 equation:

(F)=12/F-23

We move all terms to the left:

(F)-(12/F-23)=0


Domain of the equation: F-23)!=0

F∈R


We get rid of parentheses

F-12/F+23=0

We multiply all the terms by the denominator


F*F+23*F-12=0

We add all the numbers together, and all the variables

23F+F*F-12=0

Wy multiply elements

F^2+23F-12=0

a = 1; b = 23; c = -12;
Δ = b2-4ac
Δ = 232-4·1·(-12)
Δ = 577
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{-(23)-\sqrt{577}}{2*1}=\frac{-23-\sqrt{577}}{2}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(23)+\sqrt{577}}{2*1}=\frac{-23+\sqrt{577}}{2}
$