F(x)=1/3x+5

Solution for F(x)=1/3x+5 equation:

(F)=1/3F+5

We move all terms to the left:

(F)-(1/3F+5)=0


Domain of the equation: 3F+5)!=0

F∈R


We get rid of parentheses

F-1/3F-5=0

We multiply all the terms by the denominator


F*3F-5*3F-1=0

Wy multiply elements

3F^2-15F-1=0

a = 3; b = -15; c = -1;
Δ = b2-4ac
Δ = -152-4·3·(-1)
Δ = 237
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{-(-15)-\sqrt{237}}{2*3}=\frac{15-\sqrt{237}}{6}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+\sqrt{237}}{2*3}=\frac{15+\sqrt{237}}{6}
$