-21=10.75t-5t^2

Solution for -21=10.75t-5t^2 equation:

-21=10.75t-5t^2

We move all terms to the left:

-21-(10.75t-5t^2)=0

We get rid of parentheses

5t^2-10.75t-21=0

a = 5; b = -10.75; c = -21;
Δ = b2-4ac
Δ = -10.752-4·5·(-21)
Δ = 535.5625
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{-(-10.75)-\sqrt{535.5625}}{2*5}=\frac{10.75-\sqrt{535.5625}}{10}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10.75)+\sqrt{535.5625}}{2*5}=\frac{10.75+\sqrt{535.5625}}{10}
$