F(x)=7/3x-9

Solution for F(x)=7/3x-9 equation:

(F)=7/3F-9

We move all terms to the left:

(F)-(7/3F-9)=0


Domain of the equation: 3F-9)!=0

F∈R


We get rid of parentheses

F-7/3F+9=0

We multiply all the terms by the denominator


F*3F+9*3F-7=0

Wy multiply elements

3F^2+27F-7=0

a = 3; b = 27; c = -7;
Δ = b2-4ac
Δ = 272-4·3·(-7)
Δ = 813
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{-(27)-\sqrt{813}}{2*3}=\frac{-27-\sqrt{813}}{6}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+\sqrt{813}}{2*3}=\frac{-27+\sqrt{813}}{6}
$