80=3t2-30t+135

Solution for 80=3t2-30t+135 equation:

80=3t^2-30t+135

We move all terms to the left:

80-(3t^2-30t+135)=0

We get rid of parentheses

-3t^2+30t-135+80=0

We add all the numbers together, and all the variables

-3t^2+30t-55=0

a = -3; b = 30; c = -55;
Δ = b2-4ac
Δ = 302-4·(-3)·(-55)
Δ = 240
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:

$\sqrt{\Delta}=\sqrt{240}=\sqrt{16*15}=\sqrt{16}*\sqrt{15}=4\sqrt{15}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-4\sqrt{15}}{2*-3}=\frac{-30-4\sqrt{15}}{-6}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+4\sqrt{15}}{2*-3}=\frac{-30+4\sqrt{15}}{-6}
$