F(0)=6x^2+6x-5

Solution for F(0)=6x^2+6x-5 equation:

(0)=6F^2+6F-5

We move all terms to the left:

(0)-(6F^2+6F-5)=0

We add all the numbers together, and all the variables

-(6F^2+6F-5)=0

We get rid of parentheses

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

a = -6; b = -6; c = +5;
Δ = b2-4ac
Δ = -62-4·(-6)·5
Δ = 156
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:

$\sqrt{\Delta}=\sqrt{156}=\sqrt{4*39}=\sqrt{4}*\sqrt{39}=2\sqrt{39}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{39}}{2*-6}=\frac{6-2\sqrt{39}}{-12}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{39}}{2*-6}=\frac{6+2\sqrt{39}}{-12}
$