Y=16x^2+59x+20

Solution for Y=16x^2+59x+20 equation:

=16Y^2+59Y+20

We move all terms to the left:

-(16Y^2+59Y+20)=0

We get rid of parentheses

-16Y^2-59Y-20=0

a = -16; b = -59; c = -20;
Δ = b2-4ac
Δ = -592-4·(-16)·(-20)
Δ = 2201
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-59)-\sqrt{2201}}{2*-16}=\frac{59-\sqrt{2201}}{-32}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-59)+\sqrt{2201}}{2*-16}=\frac{59+\sqrt{2201}}{-32}
$