F(x)=-2x^2-4x+7

Solution for F(x)=-2x^2-4x+7 equation:

(F)=-2F^2-4F+7

We move all terms to the left:

(F)-(-2F^2-4F+7)=0

We get rid of parentheses

2F^2+4F+F-7=0

We add all the numbers together, and all the variables

2F^2+5F-7=0

a = 2; b = 5; c = -7;
Δ = b2-4ac
Δ = 52-4·2·(-7)
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-9}{2*2}=\frac{-14}{4}
=-3+1/2
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+9}{2*2}=\frac{4}{4}
=1
$