0=-16x^2+80x+4.5

Solution for 0=-16x^2+80x+4.5 equation:

0=-16x^2+80x+4.5

We move all terms to the left:

0-(-16x^2+80x+4.5)=0

We add all the numbers together, and all the variables

-(-16x^2+80x+4.5)=0

We get rid of parentheses

16x^2-80x-4.5=0

a = 16; b = -80; c = -4.5;
Δ = b2-4ac
Δ = -802-4·16·(-4.5)
Δ = 6688
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{6688}=\sqrt{16*418}=\sqrt{16}*\sqrt{418}=4\sqrt{418}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-80)-4\sqrt{418}}{2*16}=\frac{80-4\sqrt{418}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-80)+4\sqrt{418}}{2*16}=\frac{80+4\sqrt{418}}{32}
$