5400=t+13.5t^2

Solution for 5400=t+13.5t^2 equation:

5400=t+13.5t^2

We move all terms to the left:

5400-(t+13.5t^2)=0

We get rid of parentheses

-13.5t^2-t+5400=0

We add all the numbers together, and all the variables

-13.5t^2-1t+5400=0

a = -13.5; b = -1; c = +5400;
Δ = b2-4ac
Δ = -12-4·(-13.5)·5400
Δ = 291601
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:

$\sqrt{\Delta}=\sqrt{291601}=\sqrt{289*1009}=\sqrt{289}*\sqrt{1009}=17\sqrt{1009}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-17\sqrt{1009}}{2*-13.5}=\frac{1-17\sqrt{1009}}{-27}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+17\sqrt{1009}}{2*-13.5}=\frac{1+17\sqrt{1009}}{-27}
$