F(x)=-2x^2-10x+5

Solution for F(x)=-2x^2-10x+5 equation:

(F)=-2F^2-10F+5

We move all terms to the left:

(F)-(-2F^2-10F+5)=0

We get rid of parentheses

2F^2+10F+F-5=0

We add all the numbers together, and all the variables

2F^2+11F-5=0

a = 2; b = 11; c = -5;
Δ = b2-4ac
Δ = 112-4·2·(-5)
Δ = 161
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{-(11)-\sqrt{161}}{2*2}=\frac{-11-\sqrt{161}}{4}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+\sqrt{161}}{2*2}=\frac{-11+\sqrt{161}}{4}
$