F(x)=4x^2-16x+3

Solution for F(x)=4x^2-16x+3 equation:

(F)=4F^2-16F+3

We move all terms to the left:

(F)-(4F^2-16F+3)=0

We get rid of parentheses

-4F^2+F+16F-3=0

We add all the numbers together, and all the variables

-4F^2+17F-3=0

a = -4; b = 17; c = -3;
Δ = b2-4ac
Δ = 172-4·(-4)·(-3)
Δ = 241
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{-(17)-\sqrt{241}}{2*-4}=\frac{-17-\sqrt{241}}{-8}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+\sqrt{241}}{2*-4}=\frac{-17+\sqrt{241}}{-8}
$