84=4t^2+16t

Solution for 84=4t^2+16t equation:

84=4t^2+16t

We move all terms to the left:

84-(4t^2+16t)=0

We get rid of parentheses

-4t^2-16t+84=0

a = -4; b = -16; c = +84;
Δ = b2-4ac
Δ = -162-4·(-4)·84
Δ = 1600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1600}=40$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-40}{2*-4}=\frac{-24}{-8}
=+3
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+40}{2*-4}=\frac{56}{-8}
=-7
$