Y=16x^2-20x-5

Solution for Y=16x^2-20x-5 equation:

=16Y^2-20Y-5

We move all terms to the left:

-(16Y^2-20Y-5)=0

We get rid of parentheses

-16Y^2+20Y+5=0

a = -16; b = 20; c = +5;
Δ = b2-4ac
Δ = 202-4·(-16)·5
Δ = 720
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:

$\sqrt{\Delta}=\sqrt{720}=\sqrt{144*5}=\sqrt{144}*\sqrt{5}=12\sqrt{5}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-12\sqrt{5}}{2*-16}=\frac{-20-12\sqrt{5}}{-32}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+12\sqrt{5}}{2*-16}=\frac{-20+12\sqrt{5}}{-32}
$