F(x)=-2x^2+-9x+-5

Solution for F(x)=-2x^2+-9x+-5 equation:

(F)=-2F^2+-9F+-5

We move all terms to the left:

(F)-(-2F^2+-9F+-5)=0

We use the square of the difference formula

-(-2F^2-9F-5)+F=0

We get rid of parentheses

2F^2+9F+F+5=0

We add all the numbers together, and all the variables

2F^2+10F+5=0

a = 2; b = 10; c = +5;
Δ = b2-4ac
Δ = 102-4·2·5
Δ = 60
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:

$\sqrt{\Delta}=\sqrt{60}=\sqrt{4*15}=\sqrt{4}*\sqrt{15}=2\sqrt{15}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{15}}{2*2}=\frac{-10-2\sqrt{15}}{4}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{15}}{2*2}=\frac{-10+2\sqrt{15}}{4}
$