12t-t^2=32

Solution for 12t-t^2=32 equation:

12t-t^2=32

We move all terms to the left:

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

We add all the numbers together, and all the variables

-1t^2+12t-32=0

a = -1; b = 12; c = -32;
Δ = b2-4ac
Δ = 122-4·(-1)·(-32)
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-4}{2*-1}=\frac{-16}{-2}
=+8
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+4}{2*-1}=\frac{-8}{-2}
=+4
$