F(x)=2x-4x2-5x+9

Solution for F(x)=2x-4x2-5x+9 equation:

(F)=2F-4F^2-5F+9

We move all terms to the left:

(F)-(2F-4F^2-5F+9)=0

We get rid of parentheses

4F^2-2F+5F+F-9=0

We add all the numbers together, and all the variables

4F^2+4F-9=0

a = 4; b = 4; c = -9;
Δ = b2-4ac
Δ = 42-4·4·(-9)
Δ = 160
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:

$\sqrt{\Delta}=\sqrt{160}=\sqrt{16*10}=\sqrt{16}*\sqrt{10}=4\sqrt{10}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{10}}{2*4}=\frac{-4-4\sqrt{10}}{8}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{10}}{2*4}=\frac{-4+4\sqrt{10}}{8}
$