t(80-16t)=30

Solution for t(80-16t)=30 equation:

t(80-16t)=30

We move all terms to the left:

t(80-16t)-(30)=0

We add all the numbers together, and all the variables

t(-16t+80)-30=0

We multiply parentheses

-16t^2+80t-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:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

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