F(x)=1/3x+17

Solution for F(x)=1/3x+17 equation:

(F)=1/3F+17

We move all terms to the left:

(F)-(1/3F+17)=0


Domain of the equation: 3F+17)!=0

F∈R


We get rid of parentheses

F-1/3F-17=0

We multiply all the terms by the denominator


F*3F-17*3F-1=0

Wy multiply elements

3F^2-51F-1=0

a = 3; b = -51; c = -1;
Δ = b2-4ac
Δ = -512-4·3·(-1)
Δ = 2613
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{-(-51)-\sqrt{2613}}{2*3}=\frac{51-\sqrt{2613}}{6}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-51)+\sqrt{2613}}{2*3}=\frac{51+\sqrt{2613}}{6}
$