F(x)=3x^2-5x-6

Solution for F(x)=3x^2-5x-6 equation:

(F)=3F^2-5F-6

We move all terms to the left:

(F)-(3F^2-5F-6)=0

We get rid of parentheses

-3F^2+F+5F+6=0

We add all the numbers together, and all the variables

-3F^2+6F+6=0

a = -3; b = 6; c = +6;
Δ = b2-4ac
Δ = 62-4·(-3)·6
Δ = 108
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:

$\sqrt{\Delta}=\sqrt{108}=\sqrt{36*3}=\sqrt{36}*\sqrt{3}=6\sqrt{3}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6\sqrt{3}}{2*-3}=\frac{-6-6\sqrt{3}}{-6}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6\sqrt{3}}{2*-3}=\frac{-6+6\sqrt{3}}{-6}
$