F(10)=3x^2+9x-12

Solution for F(10)=3x^2+9x-12 equation:

(10)=3F^2+9F-12

We move all terms to the left:

(10)-(3F^2+9F-12)=0

We get rid of parentheses

-3F^2-9F+12+10=0

We add all the numbers together, and all the variables

-3F^2-9F+22=0

a = -3; b = -9; c = +22;
Δ = b2-4ac
Δ = -92-4·(-3)·22
Δ = 345
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{-(-9)-\sqrt{345}}{2*-3}=\frac{9-\sqrt{345}}{-6}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{345}}{2*-3}=\frac{9+\sqrt{345}}{-6}
$