F(x)=-2x^2-2x+10

Solution for F(x)=-2x^2-2x+10 equation:

(F)=-2F^2-2F+10

We move all terms to the left:

(F)-(-2F^2-2F+10)=0

We get rid of parentheses

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

We add all the numbers together, and all the variables

2F^2+3F-10=0

a = 2; b = 3; c = -10;
Δ = b2-4ac
Δ = 32-4·2·(-10)
Δ = 89
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-\sqrt{89}}{2*2}=\frac{-3-\sqrt{89}}{4}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{89}}{2*2}=\frac{-3+\sqrt{89}}{4}
$