F(-2)=4x^2+3x-8

Solution for F(-2)=4x^2+3x-8 equation:

(-2)=4F^2+3F-8

We move all terms to the left:

(-2)-(4F^2+3F-8)=0

We add all the numbers together, and all the variables

-(4F^2+3F-8)-2=0

We get rid of parentheses

-4F^2-3F+8-2=0

We add all the numbers together, and all the variables

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

a = -4; b = -3; c = +6;
Δ = b2-4ac
Δ = -32-4·(-4)·6
Δ = 105
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{-(-3)-\sqrt{105}}{2*-4}=\frac{3-\sqrt{105}}{-8}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{105}}{2*-4}=\frac{3+\sqrt{105}}{-8}
$