0=4.9t^2+400t-150

Solution for 0=4.9t^2+400t-150 equation:

0=4.9t^2+400t-150

We move all terms to the left:

0-(4.9t^2+400t-150)=0

We add all the numbers together, and all the variables

-(4.9t^2+400t-150)=0

We get rid of parentheses

-4.9t^2-400t+150=0

a = -4.9; b = -400; c = +150;
Δ = b2-4ac
Δ = -4002-4·(-4.9)·150
Δ = 162940
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:

$\sqrt{\Delta}=\sqrt{162940}=\sqrt{4*40735}=\sqrt{4}*\sqrt{40735}=2\sqrt{40735}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-400)-2\sqrt{40735}}{2*-4.9}=\frac{400-2\sqrt{40735}}{-9.8}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-400)+2\sqrt{40735}}{2*-4.9}=\frac{400+2\sqrt{40735}}{-9.8}
$