0=-4.9t^2+42t+2.5

Solution for 0=-4.9t^2+42t+2.5 equation:

0=-4.9t^2+42t+2.5

We move all terms to the left:

0-(-4.9t^2+42t+2.5)=0

We add all the numbers together, and all the variables

-(-4.9t^2+42t+2.5)=0

We get rid of parentheses

4.9t^2-42t-2.5=0

a = 4.9; b = -42; c = -2.5;
Δ = b2-4ac
Δ = -422-4·4.9·(-2.5)
Δ = 1813
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:

$\sqrt{\Delta}=\sqrt{1813}=\sqrt{49*37}=\sqrt{49}*\sqrt{37}=7\sqrt{37}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-7\sqrt{37}}{2*4.9}=\frac{42-7\sqrt{37}}{9.8}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+7\sqrt{37}}{2*4.9}=\frac{42+7\sqrt{37}}{9.8}
$