F(6)=4x^2+5x-9

Solution for F(6)=4x^2+5x-9 equation:

(6)=4F^2+5F-9

We move all terms to the left:

(6)-(4F^2+5F-9)=0

We get rid of parentheses

-4F^2-5F+9+6=0

We add all the numbers together, and all the variables

-4F^2-5F+15=0

a = -4; b = -5; c = +15;
Δ = b2-4ac
Δ = -52-4·(-4)·15
Δ = 265
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{-(-5)-\sqrt{265}}{2*-4}=\frac{5-\sqrt{265}}{-8}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{265}}{2*-4}=\frac{5+\sqrt{265}}{-8}
$