16=26t-5t^2

Solution for 16=26t-5t^2 equation:

16=26t-5t^2

We move all terms to the left:

16-(26t-5t^2)=0

We get rid of parentheses

5t^2-26t+16=0

a = 5; b = -26; c = +16;
Δ = b2-4ac
Δ = -262-4·5·16
Δ = 356
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:

$\sqrt{\Delta}=\sqrt{356}=\sqrt{4*89}=\sqrt{4}*\sqrt{89}=2\sqrt{89}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-26)-2\sqrt{89}}{2*5}=\frac{26-2\sqrt{89}}{10}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-26)+2\sqrt{89}}{2*5}=\frac{26+2\sqrt{89}}{10}
$