12=10t-2t^2

Solution for 12=10t-2t^2 equation:

12=10t-2t^2

We move all terms to the left:

12-(10t-2t^2)=0

We get rid of parentheses

2t^2-10t+12=0

a = 2; b = -10; c = +12;
Δ = b2-4ac
Δ = -102-4·2·12
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2}{2*2}=\frac{8}{4}
=2
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2}{2*2}=\frac{12}{4}
=3
$