F(-3)=4x^2+5x-6

Solution for F(-3)=4x^2+5x-6 equation:

(-3)=4F^2+5F-6

We move all terms to the left:

(-3)-(4F^2+5F-6)=0

We add all the numbers together, and all the variables

-(4F^2+5F-6)-3=0

We get rid of parentheses

-4F^2-5F+6-3=0

We add all the numbers together, and all the variables

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

a = -4; b = -5; c = +3;
Δ = b2-4ac
Δ = -52-4·(-4)·3
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*-4}=\frac{5-\sqrt{73}}{-8}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{73}}{2*-4}=\frac{5+\sqrt{73}}{-8}
$