F(-2)=3x^2+5x-6

Solution for F(-2)=3x^2+5x-6 equation:

(-2)=3F^2+5F-6

We move all terms to the left:

(-2)-(3F^2+5F-6)=0

We add all the numbers together, and all the variables

-(3F^2+5F-6)-2=0

We get rid of parentheses

-3F^2-5F+6-2=0

We add all the numbers together, and all the variables

-3F^2-5F+4=0

a = -3; b = -5; c = +4;
Δ = b2-4ac
Δ = -52-4·(-3)·4
Δ = 73
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{-(-5)-\sqrt{73}}{2*-3}=\frac{5-\sqrt{73}}{-6}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{73}}{2*-3}=\frac{5+\sqrt{73}}{-6}
$