F(-3)=6x2-12

Solution for F(-3)=6x2-12 equation:

(-3)=6F^2-12

We move all terms to the left:

(-3)-(6F^2-12)=0

We add all the numbers together, and all the variables

-(6F^2-12)-3=0

We get rid of parentheses

-6F^2+12-3=0

We add all the numbers together, and all the variables

-6F^2+9=0

a = -6; b = 0; c = +9;
Δ = b2-4ac
Δ = 02-4·(-6)·9
Δ = 216
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:

$\sqrt{\Delta}=\sqrt{216}=\sqrt{36*6}=\sqrt{36}*\sqrt{6}=6\sqrt{6}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{6}}{2*-6}=\frac{0-6\sqrt{6}}{-12}
=-\frac{6\sqrt{6}}{-12}
=-\frac{\sqrt{6}}{-2}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{6}}{2*-6}=\frac{0+6\sqrt{6}}{-12}
=\frac{6\sqrt{6}}{-12}
=\frac{\sqrt{6}}{-2}
$