4t^2=80t+84

Solution for 4t^2=80t+84 equation:

4t^2=80t+84

We move all terms to the left:

4t^2-(80t+84)=0

We get rid of parentheses

4t^2-80t-84=0

a = 4; b = -80; c = -84;
Δ = b2-4ac
Δ = -802-4·4·(-84)
Δ = 7744
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{7744}=88$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-80)-88}{2*4}=\frac{-8}{8}
=-1
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-80)+88}{2*4}=\frac{168}{8}
=21
$