F(-4)=2x^2+6x-102

Solution for F(-4)=2x^2+6x-102 equation:

(-4)=2F^2+6F-102

We move all terms to the left:

(-4)-(2F^2+6F-102)=0

We add all the numbers together, and all the variables

-(2F^2+6F-102)-4=0

We get rid of parentheses

-2F^2-6F+102-4=0

We add all the numbers together, and all the variables

-2F^2-6F+98=0

a = -2; b = -6; c = +98;
Δ = b2-4ac
Δ = -62-4·(-2)·98
Δ = 820
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:

$\sqrt{\Delta}=\sqrt{820}=\sqrt{4*205}=\sqrt{4}*\sqrt{205}=2\sqrt{205}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{205}}{2*-2}=\frac{6-2\sqrt{205}}{-4}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{205}}{2*-2}=\frac{6+2\sqrt{205}}{-4}
$