12=-4.9t^2+24.5t+11.5

Solution for 12=-4.9t^2+24.5t+11.5 equation:

12=-4.9t^2+24.5t+11.5

We move all terms to the left:

12-(-4.9t^2+24.5t+11.5)=0

We get rid of parentheses

4.9t^2-24.5t-11.5+12=0

We add all the numbers together, and all the variables

4.9t^2-24.5t+0.5=0

a = 4.9; b = -24.5; c = +0.5;
Δ = b2-4ac
Δ = -24.52-4·4.9·0.5
Δ = 590.45
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{-(-24.5)-\sqrt{590.45}}{2*4.9}=\frac{24.5-\sqrt{590.45}}{9.8}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24.5)+\sqrt{590.45}}{2*4.9}=\frac{24.5+\sqrt{590.45}}{9.8}
$