Y=5+72x-16x^2

Solution for Y=5+72x-16x^2 equation:

=5+72Y-16Y^2

We move all terms to the left:

-(5+72Y-16Y^2)=0

We get rid of parentheses

16Y^2-72Y-5=0

a = 16; b = -72; c = -5;
Δ = b2-4ac
Δ = -722-4·16·(-5)
Δ = 5504
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:

$\sqrt{\Delta}=\sqrt{5504}=\sqrt{64*86}=\sqrt{64}*\sqrt{86}=8\sqrt{86}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-72)-8\sqrt{86}}{2*16}=\frac{72-8\sqrt{86}}{32}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-72)+8\sqrt{86}}{2*16}=\frac{72+8\sqrt{86}}{32}
$