58=175-16t^2

Solution for 58=175-16t^2 equation:

58=175-16t^2

We move all terms to the left:

58-(175-16t^2)=0

We get rid of parentheses

16t^2-175+58=0

We add all the numbers together, and all the variables

16t^2-117=0

a = 16; b = 0; c = -117;
Δ = b2-4ac
Δ = 02-4·16·(-117)
Δ = 7488
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:

$\sqrt{\Delta}=\sqrt{7488}=\sqrt{576*13}=\sqrt{576}*\sqrt{13}=24\sqrt{13}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-24\sqrt{13}}{2*16}=\frac{0-24\sqrt{13}}{32}
=-\frac{24\sqrt{13}}{32}
=-\frac{3\sqrt{13}}{4}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+24\sqrt{13}}{2*16}=\frac{0+24\sqrt{13}}{32}
=\frac{24\sqrt{13}}{32}
=\frac{3\sqrt{13}}{4}
$