F(x)=3x^2-12x-63

Solution for F(x)=3x^2-12x-63 equation:

(F)=3F^2-12F-63

We move all terms to the left:

(F)-(3F^2-12F-63)=0

We get rid of parentheses

-3F^2+F+12F+63=0

We add all the numbers together, and all the variables

-3F^2+13F+63=0

a = -3; b = 13; c = +63;
Δ = b2-4ac
Δ = 132-4·(-3)·63
Δ = 925
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:

$\sqrt{\Delta}=\sqrt{925}=\sqrt{25*37}=\sqrt{25}*\sqrt{37}=5\sqrt{37}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-5\sqrt{37}}{2*-3}=\frac{-13-5\sqrt{37}}{-6}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+5\sqrt{37}}{2*-3}=\frac{-13+5\sqrt{37}}{-6}
$