F(x)=-1/3x+4

Solution for F(x)=-1/3x+4 equation:

(F)=-1/3F+4

We move all terms to the left:

(F)-(-1/3F+4)=0


Domain of the equation: 3F+4)!=0

F∈R


We get rid of parentheses

F+1/3F-4=0

We multiply all the terms by the denominator


F*3F-4*3F+1=0

Wy multiply elements

3F^2-12F+1=0

a = 3; b = -12; c = +1;
Δ = b2-4ac
Δ = -122-4·3·1
Δ = 132
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:

$\sqrt{\Delta}=\sqrt{132}=\sqrt{4*33}=\sqrt{4}*\sqrt{33}=2\sqrt{33}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{33}}{2*3}=\frac{12-2\sqrt{33}}{6}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{33}}{2*3}=\frac{12+2\sqrt{33}}{6}
$