F(x)=6x2+6x-1

Solution for F(x)=6x2+6x-1 equation:

(F)=6F^2+6F-1

We move all terms to the left:

(F)-(6F^2+6F-1)=0

We get rid of parentheses

-6F^2+F-6F+1=0

We add all the numbers together, and all the variables

-6F^2-5F+1=0

a = -6; b = -5; c = +1;
Δ = b2-4ac
Δ = -52-4·(-6)·1
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-7}{2*-6}=\frac{-2}{-12}
=1/6
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+7}{2*-6}=\frac{12}{-12}
=-1
$