175=4.9*t^2

Solution for 175=4.9*t^2 equation:

175=4.9t^2

We move all terms to the left:

175-(4.9t^2)=0

We get rid of parentheses

-4.9t^2+175=0

a = -4.9; b = 0; c = +175;
Δ = b2-4ac
Δ = 02-4·(-4.9)·175
Δ = 3430
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:

$\sqrt{\Delta}=\sqrt{3430}=\sqrt{1*3430}=\sqrt{1}*\sqrt{3430}=1\sqrt{3430}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-1\sqrt{3430}}{2*-4.9}=\frac{0-1\sqrt{3430}}{-9.8}
=-\frac{1\sqrt{3430}}{-9.8}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+1\sqrt{3430}}{2*-4.9}=\frac{0+1\sqrt{3430}}{-9.8}
=\frac{1\sqrt{3430}}{-9.8}
$