90=100t-5t^2

Solution for 90=100t-5t^2 equation:

90=100t-5t^2

We move all terms to the left:

90-(100t-5t^2)=0

We get rid of parentheses

5t^2-100t+90=0

a = 5; b = -100; c = +90;
Δ = b2-4ac
Δ = -1002-4·5·90
Δ = 8200
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:

$\sqrt{\Delta}=\sqrt{8200}=\sqrt{100*82}=\sqrt{100}*\sqrt{82}=10\sqrt{82}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-100)-10\sqrt{82}}{2*5}=\frac{100-10\sqrt{82}}{10}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-100)+10\sqrt{82}}{2*5}=\frac{100+10\sqrt{82}}{10}
$