F(x)=3x^2-10x-9

Solution for F(x)=3x^2-10x-9 equation:

(F)=3F^2-10F-9

We move all terms to the left:

(F)-(3F^2-10F-9)=0

We get rid of parentheses

-3F^2+F+10F+9=0

We add all the numbers together, and all the variables

-3F^2+11F+9=0

a = -3; b = 11; c = +9;
Δ = b2-4ac
Δ = 112-4·(-3)·9
Δ = 229
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{-(11)-\sqrt{229}}{2*-3}=\frac{-11-\sqrt{229}}{-6}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+\sqrt{229}}{2*-3}=\frac{-11+\sqrt{229}}{-6}
$