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

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

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

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

4F^2-1F-3=0

a = 4; b = -1; c = -3;
Δ = b2-4ac
Δ = -12-4·4·(-3)
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{-(-1)-7}{2*4}=\frac{-6}{8}
=-3/4
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+7}{2*4}=\frac{8}{8}
=1
$