100=30t+5t^2

Solution for 100=30t+5t^2 equation:

100=30t+5t^2

We move all terms to the left:

100-(30t+5t^2)=0

We get rid of parentheses

-5t^2-30t+100=0

a = -5; b = -30; c = +100;
Δ = b2-4ac
Δ = -302-4·(-5)·100
Δ = 2900
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:

$\sqrt{\Delta}=\sqrt{2900}=\sqrt{100*29}=\sqrt{100}*\sqrt{29}=10\sqrt{29}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-10\sqrt{29}}{2*-5}=\frac{30-10\sqrt{29}}{-10}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+10\sqrt{29}}{2*-5}=\frac{30+10\sqrt{29}}{-10}
$