F(x)=4x^2-2x-9

Solution for F(x)=4x^2-2x-9 equation:

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

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-4F^2+3F+9=0

a = -4; b = 3; c = +9;
Δ = b2-4ac
Δ = 32-4·(-4)·9
Δ = 153
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:

$\sqrt{\Delta}=\sqrt{153}=\sqrt{9*17}=\sqrt{9}*\sqrt{17}=3\sqrt{17}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3\sqrt{17}}{2*-4}=\frac{-3-3\sqrt{17}}{-8}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3\sqrt{17}}{2*-4}=\frac{-3+3\sqrt{17}}{-8}
$