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+F+2F+3=0

We add all the numbers together, and all the variables

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

a = -4; b = 3; c = +3;
Δ = b2-4ac
Δ = 32-4·(-4)·3
Δ = 57
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{-(3)-\sqrt{57}}{2*-4}=\frac{-3-\sqrt{57}}{-8}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{57}}{2*-4}=\frac{-3+\sqrt{57}}{-8}
$