F(x)=2/3x+3

Solution for F(x)=2/3x+3 equation:

(F)=2/3F+3

We move all terms to the left:

(F)-(2/3F+3)=0


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

F∈R


We get rid of parentheses

F-2/3F-3=0

We multiply all the terms by the denominator


F*3F-3*3F-2=0

Wy multiply elements

3F^2-9F-2=0

a = 3; b = -9; c = -2;
Δ = b2-4ac
Δ = -92-4·3·(-2)
Δ = 105
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{-(-9)-\sqrt{105}}{2*3}=\frac{9-\sqrt{105}}{6}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{105}}{2*3}=\frac{9+\sqrt{105}}{6}
$