F(-4)=-4x^2-3x+6

Solution for F(-4)=-4x^2-3x+6 equation:

(-4)=-4F^2-3F+6

We move all terms to the left:

(-4)-(-4F^2-3F+6)=0

We add all the numbers together, and all the variables

-(-4F^2-3F+6)-4=0

We get rid of parentheses

4F^2+3F-6-4=0

We add all the numbers together, and all the variables

4F^2+3F-10=0

a = 4; b = 3; c = -10;
Δ = b2-4ac
Δ = 32-4·4·(-10)
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-13}{2*4}=\frac{-16}{8}
=-2
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+13}{2*4}=\frac{10}{8}
=1+1/4
$