F(x)=12-1/2x

Solution for F(x)=12-1/2x equation:

(F)=12-1/2F

We move all terms to the left:

(F)-(12-1/2F)=0


Domain of the equation: 2F)!=0

F!=0/1

F!=0

F∈R


We add all the numbers together, and all the variables

F-(-1/2F+12)=0

We get rid of parentheses

F+1/2F-12=0

We multiply all the terms by the denominator


F*2F-12*2F+1=0

Wy multiply elements

2F^2-24F+1=0

a = 2; b = -24; c = +1;
Δ = b2-4ac
Δ = -242-4·2·1
Δ = 568
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:

$\sqrt{\Delta}=\sqrt{568}=\sqrt{4*142}=\sqrt{4}*\sqrt{142}=2\sqrt{142}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-2\sqrt{142}}{2*2}=\frac{24-2\sqrt{142}}{4}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+2\sqrt{142}}{2*2}=\frac{24+2\sqrt{142}}{4}
$