Y=4n^2-17n+4

Solution for Y=4n^2-17n+4 equation:

=4Y^2-17Y+4

We move all terms to the left:

-(4Y^2-17Y+4)=0

We get rid of parentheses

-4Y^2+17Y-4=0

a = -4; b = 17; c = -4;
Δ = b2-4ac
Δ = 172-4·(-4)·(-4)
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-15}{2*-4}=\frac{-32}{-8}
=+4
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+15}{2*-4}=\frac{-2}{-8}
=1/4
$