17.32=20t+5t^2

Solution for 17.32=20t+5t^2 equation:

17.32=20t+5t^2

We move all terms to the left:

17.32-(20t+5t^2)=0

We get rid of parentheses

-5t^2-20t+17.32=0

a = -5; b = -20; c = +17.32;
Δ = b2-4ac
Δ = -202-4·(-5)·17.32
Δ = 746.4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-\sqrt{746.4}}{2*-5}=\frac{20-\sqrt{746.4}}{-10}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+\sqrt{746.4}}{2*-5}=\frac{20+\sqrt{746.4}}{-10}
$