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 = 348
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:

$\sqrt{\Delta}=\sqrt{348}=\sqrt{4*87}=\sqrt{4}*\sqrt{87}=2\sqrt{87}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-2\sqrt{87}}{2*3}=\frac{-18-2\sqrt{87}}{6}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+2\sqrt{87}}{2*3}=\frac{-18+2\sqrt{87}}{6}
$