F(-2)=2x^2+3x-7

Solution for F(-2)=2x^2+3x-7 equation:

(-2)=2F^2+3F-7

We move all terms to the left:

(-2)-(2F^2+3F-7)=0

We add all the numbers together, and all the variables

-(2F^2+3F-7)-2=0

We get rid of parentheses

-2F^2-3F+7-2=0

We add all the numbers together, and all the variables

-2F^2-3F+5=0

a = -2; b = -3; c = +5;
Δ = b2-4ac
Δ = -32-4·(-2)·5
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-7}{2*-2}=\frac{-4}{-4}
=1
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+7}{2*-2}=\frac{10}{-4}
=-2+1/2
$