10=90t-16t^2

Solution for 10=90t-16t^2 equation:

10=90t-16t^2

We move all terms to the left:

10-(90t-16t^2)=0

We get rid of parentheses

16t^2-90t+10=0

a = 16; b = -90; c = +10;
Δ = b2-4ac
Δ = -902-4·16·10
Δ = 7460
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:

$\sqrt{\Delta}=\sqrt{7460}=\sqrt{4*1865}=\sqrt{4}*\sqrt{1865}=2\sqrt{1865}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-90)-2\sqrt{1865}}{2*16}=\frac{90-2\sqrt{1865}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-90)+2\sqrt{1865}}{2*16}=\frac{90+2\sqrt{1865}}{32}
$