12=35t-5t^2

Solution for 12=35t-5t^2 equation:

12=35t-5t^2

We move all terms to the left:

12-(35t-5t^2)=0

We get rid of parentheses

5t^2-35t+12=0

a = 5; b = -35; c = +12;
Δ = b2-4ac
Δ = -352-4·5·12
Δ = 985
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{-(-35)-\sqrt{985}}{2*5}=\frac{35-\sqrt{985}}{10}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-35)+\sqrt{985}}{2*5}=\frac{35+\sqrt{985}}{10}
$