(t)=-10.5t^2+84t

Solution for (t)=-10.5t^2+84t equation:

(t)=-10.5t^2+84t

We move all terms to the left:

(t)-(-10.5t^2+84t)=0

We get rid of parentheses

10.5t^2-84t+t=0

We add all the numbers together, and all the variables

10.5t^2-83t=0

a = 10.5; b = -83; c = 0;
Δ = b2-4ac
Δ = -832-4·10.5·0
Δ = 6889
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6889}=83$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-83)-83}{2*10.5}=\frac{0}{21}
=0
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-83)+83}{2*10.5}=\frac{166}{21}
=7+19/21
$