F(x)=6x^2-x-12

Solution for F(x)=6x^2-x-12 equation:

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

We move all terms to the left:

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

We get rid of parentheses

-6F^2+F+F+12=0

We add all the numbers together, and all the variables

-6F^2+2F+12=0

a = -6; b = 2; c = +12;
Δ = b2-4ac
Δ = 22-4·(-6)·12
Δ = 292
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:

$\sqrt{\Delta}=\sqrt{292}=\sqrt{4*73}=\sqrt{4}*\sqrt{73}=2\sqrt{73}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{73}}{2*-6}=\frac{-2-2\sqrt{73}}{-12}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{73}}{2*-6}=\frac{-2+2\sqrt{73}}{-12}
$