F(x)=12-3/4x

Solution for F(x)=12-3/4x equation:

(F)=12-3/4F

We move all terms to the left:

(F)-(12-3/4F)=0


Domain of the equation: 4F)!=0

F!=0/1

F!=0

F∈R


We add all the numbers together, and all the variables

F-(-3/4F+12)=0

We get rid of parentheses

F+3/4F-12=0

We multiply all the terms by the denominator


F*4F-12*4F+3=0

Wy multiply elements

4F^2-48F+3=0

a = 4; b = -48; c = +3;
Δ = b2-4ac
Δ = -482-4·4·3
Δ = 2256
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:

$\sqrt{\Delta}=\sqrt{2256}=\sqrt{16*141}=\sqrt{16}*\sqrt{141}=4\sqrt{141}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-4\sqrt{141}}{2*4}=\frac{48-4\sqrt{141}}{8}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+4\sqrt{141}}{2*4}=\frac{48+4\sqrt{141}}{8}
$