0=80t-16t^2+46

Solution for 0=80t-16t^2+46 equation:

0=80t-16t^2+46

We move all terms to the left:

0-(80t-16t^2+46)=0

We add all the numbers together, and all the variables

-(80t-16t^2+46)=0

We get rid of parentheses

16t^2-80t-46=0

a = 16; b = -80; c = -46;
Δ = b2-4ac
Δ = -802-4·16·(-46)
Δ = 9344
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{9344}=\sqrt{64*146}=\sqrt{64}*\sqrt{146}=8\sqrt{146}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-80)-8\sqrt{146}}{2*16}=\frac{80-8\sqrt{146}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-80)+8\sqrt{146}}{2*16}=\frac{80+8\sqrt{146}}{32}
$