Y=16x^2+80x+30

Solution for Y=16x^2+80x+30 equation:

=16Y^2+80Y+30

We move all terms to the left:

-(16Y^2+80Y+30)=0

We get rid of parentheses

-16Y^2-80Y-30=0

a = -16; b = -80; c = -30;
Δ = b2-4ac
Δ = -802-4·(-16)·(-30)
Δ = 4480
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:

$\sqrt{\Delta}=\sqrt{4480}=\sqrt{64*70}=\sqrt{64}*\sqrt{70}=8\sqrt{70}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-80)-8\sqrt{70}}{2*-16}=\frac{80-8\sqrt{70}}{-32}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-80)+8\sqrt{70}}{2*-16}=\frac{80+8\sqrt{70}}{-32}
$