F(-6)=x^2+3x-7

Solution for F(-6)=x^2+3x-7 equation:

(-6)=F^2+3F-7

We move all terms to the left:

(-6)-(F^2+3F-7)=0

We add all the numbers together, and all the variables

-(F^2+3F-7)-6=0

We get rid of parentheses

-F^2-3F+7-6=0

We add all the numbers together, and all the variables

-1F^2-3F+1=0

a = -1; b = -3; c = +1;
Δ = b2-4ac
Δ = -32-4·(-1)·1
Δ = 13
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{13}}{2*-1}=\frac{3-\sqrt{13}}{-2}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{13}}{2*-1}=\frac{3+\sqrt{13}}{-2}
$