50=-16t^2+124t+12

Solution for 50=-16t^2+124t+12 equation:

50=-16t^2+124t+12

We move all terms to the left:

50-(-16t^2+124t+12)=0

We get rid of parentheses

16t^2-124t-12+50=0

We add all the numbers together, and all the variables

16t^2-124t+38=0

a = 16; b = -124; c = +38;
Δ = b2-4ac
Δ = -1242-4·16·38
Δ = 12944
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{12944}=\sqrt{16*809}=\sqrt{16}*\sqrt{809}=4\sqrt{809}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-124)-4\sqrt{809}}{2*16}=\frac{124-4\sqrt{809}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-124)+4\sqrt{809}}{2*16}=\frac{124+4\sqrt{809}}{32}
$