F(x)=3x2-6

Solution for F(x)=3x2-6 equation:

(F)=3F^2-6

We move all terms to the left:

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

We get rid of parentheses

-3F^2+F+6=0

a = -3; b = 1; c = +6;
Δ = b2-4ac
Δ = 12-4·(-3)·6
Δ = 73
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{-(1)-\sqrt{73}}{2*-3}=\frac{-1-\sqrt{73}}{-6}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{73}}{2*-3}=\frac{-1+\sqrt{73}}{-6}
$