100=60t+5t^2

Solution for 100=60t+5t^2 equation:

100=60t+5t^2

We move all terms to the left:

100-(60t+5t^2)=0

We get rid of parentheses

-5t^2-60t+100=0

a = -5; b = -60; c = +100;
Δ = b2-4ac
Δ = -602-4·(-5)·100
Δ = 5600
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:

$\sqrt{\Delta}=\sqrt{5600}=\sqrt{400*14}=\sqrt{400}*\sqrt{14}=20\sqrt{14}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-20\sqrt{14}}{2*-5}=\frac{60-20\sqrt{14}}{-10}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+20\sqrt{14}}{2*-5}=\frac{60+20\sqrt{14}}{-10}
$