F(0)=-5x+27/3x-9

Solution for F(0)=-5x+27/3x-9 equation:

(0)=-5F+27/3F-9

We move all terms to the left:

(0)-(-5F+27/3F-9)=0


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

F∈R


We add all the numbers together, and all the variables

-(-5F+27/3F-9)=0

We get rid of parentheses

5F-27/3F+9=0

We multiply all the terms by the denominator


5F*3F+9*3F-27=0

Wy multiply elements

15F^2+27F-27=0

a = 15; b = 27; c = -27;
Δ = b2-4ac
Δ = 272-4·15·(-27)
Δ = 2349
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:

$\sqrt{\Delta}=\sqrt{2349}=\sqrt{81*29}=\sqrt{81}*\sqrt{29}=9\sqrt{29}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-9\sqrt{29}}{2*15}=\frac{-27-9\sqrt{29}}{30}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+9\sqrt{29}}{2*15}=\frac{-27+9\sqrt{29}}{30}
$