84=18t2+7t

Solution for 84=18t2+7t equation:

84=18t^2+7t

We move all terms to the left:

84-(18t^2+7t)=0

We get rid of parentheses

-18t^2-7t+84=0

a = -18; b = -7; c = +84;
Δ = b2-4ac
Δ = -72-4·(-18)·84
Δ = 6097
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{-(-7)-\sqrt{6097}}{2*-18}=\frac{7-\sqrt{6097}}{-36}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{6097}}{2*-18}=\frac{7+\sqrt{6097}}{-36}
$