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

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

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

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

2F^2+6F-6=0

a = 2; b = 6; c = -6;
Δ = b2-4ac
Δ = 62-4·2·(-6)
Δ = 84
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:

$\sqrt{\Delta}=\sqrt{84}=\sqrt{4*21}=\sqrt{4}*\sqrt{21}=2\sqrt{21}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{21}}{2*2}=\frac{-6-2\sqrt{21}}{4}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{21}}{2*2}=\frac{-6+2\sqrt{21}}{4}
$