Y=4x2-6x+1

Solution for Y=4x2-6x+1 equation:

=4Y^2-6Y+1

We move all terms to the left:

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

We get rid of parentheses

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

a = -4; b = 6; c = -1;
Δ = b2-4ac
Δ = 62-4·(-4)·(-1)
Δ = 20
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{20}=\sqrt{4*5}=\sqrt{4}*\sqrt{5}=2\sqrt{5}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{5}}{2*-4}=\frac{-6-2\sqrt{5}}{-8}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{5}}{2*-4}=\frac{-6+2\sqrt{5}}{-8}
$