0=4.9t^2+6t-250

Solution for 0=4.9t^2+6t-250 equation:

0=4.9t^2+6t-250

We move all terms to the left:

0-(4.9t^2+6t-250)=0

We add all the numbers together, and all the variables

-(4.9t^2+6t-250)=0

We get rid of parentheses

-4.9t^2-6t+250=0

a = -4.9; b = -6; c = +250;
Δ = b2-4ac
Δ = -62-4·(-4.9)·250
Δ = 4936
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:

$\sqrt{\Delta}=\sqrt{4936}=\sqrt{4*1234}=\sqrt{4}*\sqrt{1234}=2\sqrt{1234}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{1234}}{2*-4.9}=\frac{6-2\sqrt{1234}}{-9.8}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{1234}}{2*-4.9}=\frac{6+2\sqrt{1234}}{-9.8}
$