58=16t^2+60t+2

Solution for 58=16t^2+60t+2 equation:

58=16t^2+60t+2

We move all terms to the left:

58-(16t^2+60t+2)=0

We get rid of parentheses

-16t^2-60t-2+58=0

We add all the numbers together, and all the variables

-16t^2-60t+56=0

a = -16; b = -60; c = +56;
Δ = b2-4ac
Δ = -602-4·(-16)·56
Δ = 7184
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:

$\sqrt{\Delta}=\sqrt{7184}=\sqrt{16*449}=\sqrt{16}*\sqrt{449}=4\sqrt{449}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-4\sqrt{449}}{2*-16}=\frac{60-4\sqrt{449}}{-32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+4\sqrt{449}}{2*-16}=\frac{60+4\sqrt{449}}{-32}
$