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

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

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

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

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

a = -4; b = -2; c = +2;
Δ = b2-4ac
Δ = -22-4·(-4)·2
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-6}{2*-4}=\frac{-4}{-8}
=1/2
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+6}{2*-4}=\frac{8}{-8}
=-1
$