54t(-1t+3)=80

Solution for 54t(-1t+3)=80 equation:

54t(-1t+3)=80

We move all terms to the left:

54t(-1t+3)-(80)=0

We multiply parentheses

-54t^2+162t-80=0

a = -54; b = 162; c = -80;
Δ = b2-4ac
Δ = 1622-4·(-54)·(-80)
Δ = 8964
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:

$\sqrt{\Delta}=\sqrt{8964}=\sqrt{36*249}=\sqrt{36}*\sqrt{249}=6\sqrt{249}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(162)-6\sqrt{249}}{2*-54}=\frac{-162-6\sqrt{249}}{-108}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(162)+6\sqrt{249}}{2*-54}=\frac{-162+6\sqrt{249}}{-108}
$