100=5t^2-54t

Solution for 100=5t^2-54t equation:

100=5t^2-54t

We move all terms to the left:

100-(5t^2-54t)=0

We get rid of parentheses

-5t^2+54t+100=0

a = -5; b = 54; c = +100;
Δ = b2-4ac
Δ = 542-4·(-5)·100
Δ = 4916
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:

$\sqrt{\Delta}=\sqrt{4916}=\sqrt{4*1229}=\sqrt{4}*\sqrt{1229}=2\sqrt{1229}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(54)-2\sqrt{1229}}{2*-5}=\frac{-54-2\sqrt{1229}}{-10}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(54)+2\sqrt{1229}}{2*-5}=\frac{-54+2\sqrt{1229}}{-10}
$