F(x)=-4x^2-5x+6

Solution for F(x)=-4x^2-5x+6 equation:

(F)=-4F^2-5F+6

We move all terms to the left:

(F)-(-4F^2-5F+6)=0

We get rid of parentheses

4F^2+5F+F-6=0

We add all the numbers together, and all the variables

4F^2+6F-6=0

a = 4; b = 6; c = -6;
Δ = b2-4ac
Δ = 62-4·4·(-6)
Δ = 132
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:

$\sqrt{\Delta}=\sqrt{132}=\sqrt{4*33}=\sqrt{4}*\sqrt{33}=2\sqrt{33}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{33}}{2*4}=\frac{-6-2\sqrt{33}}{8}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{33}}{2*4}=\frac{-6+2\sqrt{33}}{8}
$