63=12t+3t^2

Solution for 63=12t+3t^2 equation:

63=12t+3t^2

We move all terms to the left:

63-(12t+3t^2)=0

We get rid of parentheses

-3t^2-12t+63=0

a = -3; b = -12; c = +63;
Δ = b2-4ac
Δ = -122-4·(-3)·63
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-30}{2*-3}=\frac{-18}{-6}
=+3
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+30}{2*-3}=\frac{42}{-6}
=-7
$