F(x)=1/2x-12

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

(F)=1/2F-12

We move all terms to the left:

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


Domain of the equation: 2F-12)!=0

F∈R


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 = 584
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:

$\sqrt{\Delta}=\sqrt{584}=\sqrt{4*146}=\sqrt{4}*\sqrt{146}=2\sqrt{146}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-2\sqrt{146}}{2*2}=\frac{-24-2\sqrt{146}}{4}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+2\sqrt{146}}{2*2}=\frac{-24+2\sqrt{146}}{4}
$