F(-9)=3x^2+5x-14

Solution for F(-9)=3x^2+5x-14 equation:

(-9)=3F^2+5F-14

We move all terms to the left:

(-9)-(3F^2+5F-14)=0

We add all the numbers together, and all the variables

-(3F^2+5F-14)-9=0

We get rid of parentheses

-3F^2-5F+14-9=0

We add all the numbers together, and all the variables

-3F^2-5F+5=0

a = -3; b = -5; c = +5;
Δ = b2-4ac
Δ = -52-4·(-3)·5
Δ = 85
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{-(-5)-\sqrt{85}}{2*-3}=\frac{5-\sqrt{85}}{-6}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{85}}{2*-3}=\frac{5+\sqrt{85}}{-6}
$