50t+1.5t2=84

Solution for 50t+1.5t2=84 equation:

50t+1.5t^2=84

We move all terms to the left:

50t+1.5t^2-(84)=0

a = 1.5; b = 50; c = -84;
Δ = b2-4ac
Δ = 502-4·1.5·(-84)
Δ = 3004
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{3004}=\sqrt{4*751}=\sqrt{4}*\sqrt{751}=2\sqrt{751}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(50)-2\sqrt{751}}{2*1.5}=\frac{-50-2\sqrt{751}}{3}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(50)+2\sqrt{751}}{2*1.5}=\frac{-50+2\sqrt{751}}{3}
$