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 = 57
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{57}}{2*3}=\frac{9-\sqrt{57}}{6}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{57}}{2*3}=\frac{9+\sqrt{57}}{6}
$