F(x)=1/4x-12

Solution for F(x)=1/4x-12 equation:

(F)=1/4F-12

We move all terms to the left:

(F)-(1/4F-12)=0


Domain of the equation: 4F-12)!=0

F∈R


We get rid of parentheses

F-1/4F+12=0

We multiply all the terms by the denominator


F*4F+12*4F-1=0

Wy multiply elements

4F^2+48F-1=0

a = 4; b = 48; c = -1;
Δ = b2-4ac
Δ = 482-4·4·(-1)
Δ = 2320
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:

$\sqrt{\Delta}=\sqrt{2320}=\sqrt{16*145}=\sqrt{16}*\sqrt{145}=4\sqrt{145}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-4\sqrt{145}}{2*4}=\frac{-48-4\sqrt{145}}{8}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+4\sqrt{145}}{2*4}=\frac{-48+4\sqrt{145}}{8}
$