F(x)=4x^2-6x+1

Solution for F(x)=4x^2-6x+1 equation:

(F)=4F^2-6F+1

We move all terms to the left:

(F)-(4F^2-6F+1)=0

We get rid of parentheses

-4F^2+F+6F-1=0

We add all the numbers together, and all the variables

-4F^2+7F-1=0

a = -4; b = 7; c = -1;
Δ = b2-4ac
Δ = 72-4·(-4)·(-1)
Δ = 33
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{-(7)-\sqrt{33}}{2*-4}=\frac{-7-\sqrt{33}}{-8}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{33}}{2*-4}=\frac{-7+\sqrt{33}}{-8}
$