F(x)=6x^2-9x-6

Solution for F(x)=6x^2-9x-6 equation:

(F)=6F^2-9F-6

We move all terms to the left:

(F)-(6F^2-9F-6)=0

We get rid of parentheses

-6F^2+F+9F+6=0

We add all the numbers together, and all the variables

-6F^2+10F+6=0

a = -6; b = 10; c = +6;
Δ = b2-4ac
Δ = 102-4·(-6)·6
Δ = 244
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:

$\sqrt{\Delta}=\sqrt{244}=\sqrt{4*61}=\sqrt{4}*\sqrt{61}=2\sqrt{61}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{61}}{2*-6}=\frac{-10-2\sqrt{61}}{-12}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{61}}{2*-6}=\frac{-10+2\sqrt{61}}{-12}
$