F(x)=6x2+12x-3

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

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

We move all terms to the left:

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

We get rid of parentheses

-6F^2+F-12F+3=0

We add all the numbers together, and all the variables

-6F^2-11F+3=0

a = -6; b = -11; c = +3;
Δ = b2-4ac
Δ = -112-4·(-6)·3
Δ = 193
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{-(-11)-\sqrt{193}}{2*-6}=\frac{11-\sqrt{193}}{-12}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{193}}{2*-6}=\frac{11+\sqrt{193}}{-12}
$