214.5=177+t+1.5t^2

Solution for 214.5=177+t+1.5t^2 equation:

214.5=177+t+1.5t^2

We move all terms to the left:

214.5-(177+t+1.5t^2)=0

We get rid of parentheses

-1.5t^2-t-177+214.5=0

We add all the numbers together, and all the variables

-1.5t^2-1t+37.5=0

a = -1.5; b = -1; c = +37.5;
Δ = b2-4ac
Δ = -12-4·(-1.5)·37.5
Δ = 226
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)-\sqrt{226}}{2*-1.5}=\frac{1-\sqrt{226}}{-3}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{226}}{2*-1.5}=\frac{1+\sqrt{226}}{-3}
$