F(x)=2/3*9x+6

Solution for F(x)=2/3*9x+6 equation:

(F)=2/3*9F+6

We move all terms to the left:

(F)-(2/3*9F+6)=0


Domain of the equation: 3*9F+6)!=0

F∈R


We get rid of parentheses

F-2/3*9F-6=0

We multiply all the terms by the denominator


F*3*9F-6*3*9F-2=0

Wy multiply elements

27F^2*9-162F*9-2=0

Wy multiply elements

243F^2-1458F-2=0

a = 243; b = -1458; c = -2;
Δ = b2-4ac
Δ = -14582-4·243·(-2)
Δ = 2127708
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:

$\sqrt{\Delta}=\sqrt{2127708}=\sqrt{324*6567}=\sqrt{324}*\sqrt{6567}=18\sqrt{6567}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1458)-18\sqrt{6567}}{2*243}=\frac{1458-18\sqrt{6567}}{486}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1458)+18\sqrt{6567}}{2*243}=\frac{1458+18\sqrt{6567}}{486}
$