F(x)=-2/3x+6

Solution for F(x)=-2/3x+6 equation:

(F)=-2/3F+6

We move all terms to the left:

(F)-(-2/3F+6)=0


Domain of the equation: 3F+6)!=0

F∈R


We get rid of parentheses

F+2/3F-6=0

We multiply all the terms by the denominator


F*3F-6*3F+2=0

Wy multiply elements

3F^2-18F+2=0

a = 3; b = -18; c = +2;
Δ = b2-4ac
Δ = -182-4·3·2
Δ = 300
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{300}=\sqrt{100*3}=\sqrt{100}*\sqrt{3}=10\sqrt{3}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-10\sqrt{3}}{2*3}=\frac{18-10\sqrt{3}}{6}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+10\sqrt{3}}{2*3}=\frac{18+10\sqrt{3}}{6}
$