0=6t^2-54t+20

Solution for 0=6t^2-54t+20 equation:

0=6t^2-54t+20

We move all terms to the left:

0-(6t^2-54t+20)=0

We add all the numbers together, and all the variables

-(6t^2-54t+20)=0

We get rid of parentheses

-6t^2+54t-20=0

a = -6; b = 54; c = -20;
Δ = b2-4ac
Δ = 542-4·(-6)·(-20)
Δ = 2436
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:

$\sqrt{\Delta}=\sqrt{2436}=\sqrt{4*609}=\sqrt{4}*\sqrt{609}=2\sqrt{609}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(54)-2\sqrt{609}}{2*-6}=\frac{-54-2\sqrt{609}}{-12}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(54)+2\sqrt{609}}{2*-6}=\frac{-54+2\sqrt{609}}{-12}
$