5.0t+1.5t2=84

Solution for 5.0t+1.5t2=84 equation:

5.0t+1.5t^2=84

We move all terms to the left:

5.0t+1.5t^2-(84)=0

a = 1.5; b = 5.0; c = -84;
Δ = b2-4ac
Δ = 5.02-4·1.5·(-84)
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5.0)-23}{2*1.5}=\frac{-28}{3}
=-9+1/3
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5.0)+23}{2*1.5}=\frac{18}{3}
=6
$