F(-1)=3x^2+5x

Solution for F(-1)=3x^2+5x equation:

(-1)=3F^2+5F

We move all terms to the left:

(-1)-(3F^2+5F)=0

We add all the numbers together, and all the variables

-(3F^2+5F)-1=0

We get rid of parentheses

-3F^2-5F-1=0

a = -3; b = -5; c = -1;
Δ = b2-4ac
Δ = -52-4·(-3)·(-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{-(-5)-\sqrt{13}}{2*-3}=\frac{5-\sqrt{13}}{-6}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{13}}{2*-3}=\frac{5+\sqrt{13}}{-6}
$