5t^2+1.5t=84

Solution for 5t^2+1.5t=84 equation:

5t^2+1.5t=84

We move all terms to the left:

5t^2+1.5t-(84)=0

a = 5; b = 1.5; c = -84;
Δ = b2-4ac
Δ = 1.52-4·5·(-84)
Δ = 1682.25
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{-(1.5)-\sqrt{1682.25}}{2*5}=\frac{-1.5-\sqrt{1682.25}}{10}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1.5)+\sqrt{1682.25}}{2*5}=\frac{-1.5+\sqrt{1682.25}}{10}
$