0=12t-5t^2+32

Solution for 0=12t-5t^2+32 equation:

0=12t-5t^2+32

We move all terms to the left:

0-(12t-5t^2+32)=0

We add all the numbers together, and all the variables

-(12t-5t^2+32)=0

We get rid of parentheses

5t^2-12t-32=0

a = 5; b = -12; c = -32;
Δ = b2-4ac
Δ = -122-4·5·(-32)
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-28}{2*5}=\frac{-16}{10}
=-1+3/5
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+28}{2*5}=\frac{40}{10}
=4
$