F(x)=-1/3x+13

Solution for F(x)=-1/3x+13 equation:

(F)=-1/3F+13

We move all terms to the left:

(F)-(-1/3F+13)=0


Domain of the equation: 3F+13)!=0

F∈R


We get rid of parentheses

F+1/3F-13=0

We multiply all the terms by the denominator


F*3F-13*3F+1=0

Wy multiply elements

3F^2-39F+1=0

a = 3; b = -39; c = +1;
Δ = b2-4ac
Δ = -392-4·3·1
Δ = 1509
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-39)-\sqrt{1509}}{2*3}=\frac{39-\sqrt{1509}}{6}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-39)+\sqrt{1509}}{2*3}=\frac{39+\sqrt{1509}}{6}
$