2=6+60t-16t^2

Solution for 2=6+60t-16t^2 equation:

2=6+60t-16t^2

We move all terms to the left:

2-(6+60t-16t^2)=0

We get rid of parentheses

16t^2-60t-6+2=0

We add all the numbers together, and all the variables

16t^2-60t-4=0

a = 16; b = -60; c = -4;
Δ = b2-4ac
Δ = -602-4·16·(-4)
Δ = 3856
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:

$\sqrt{\Delta}=\sqrt{3856}=\sqrt{16*241}=\sqrt{16}*\sqrt{241}=4\sqrt{241}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-4\sqrt{241}}{2*16}=\frac{60-4\sqrt{241}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+4\sqrt{241}}{2*16}=\frac{60+4\sqrt{241}}{32}
$