100=-4.9t^2+30t+75

Solution for 100=-4.9t^2+30t+75 equation:

100=-4.9t^2+30t+75

We move all terms to the left:

100-(-4.9t^2+30t+75)=0

We get rid of parentheses

4.9t^2-30t-75+100=0

We add all the numbers together, and all the variables

4.9t^2-30t+25=0

a = 4.9; b = -30; c = +25;
Δ = b2-4ac
Δ = -302-4·4.9·25
Δ = 410
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{-(-30)-\sqrt{410}}{2*4.9}=\frac{30-\sqrt{410}}{9.8}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+\sqrt{410}}{2*4.9}=\frac{30+\sqrt{410}}{9.8}
$