0=175+6.5t-4.9t^2

Solution for 0=175+6.5t-4.9t^2 equation:

0=175+6.5t-4.9t^2

We move all terms to the left:

0-(175+6.5t-4.9t^2)=0

We add all the numbers together, and all the variables

-(175+6.5t-4.9t^2)=0

We get rid of parentheses

4.9t^2-6.5t-175=0

a = 4.9; b = -6.5; c = -175;
Δ = b2-4ac
Δ = -6.52-4·4.9·(-175)
Δ = 3472.25
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{-(-6.5)-\sqrt{3472.25}}{2*4.9}=\frac{6.5-\sqrt{3472.25}}{9.8}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6.5)+\sqrt{3472.25}}{2*4.9}=\frac{6.5+\sqrt{3472.25}}{9.8}
$