2=4+60t+-16t^2

Solution for 2=4+60t+-16t^2 equation:

2=4+60t+-16t^2

We move all terms to the left:

2-(4+60t+-16t^2)=0

We use the square of the difference formula

-(4+60t-16t^2)+2=0

We get rid of parentheses

16t^2-60t-4+2=0

We add all the numbers together, and all the variables

16t^2-60t-2=0

a = 16; b = -60; c = -2;
Δ = b2-4ac
Δ = -602-4·16·(-2)
Δ = 3728
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:

$\sqrt{\Delta}=\sqrt{3728}=\sqrt{16*233}=\sqrt{16}*\sqrt{233}=4\sqrt{233}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-4\sqrt{233}}{2*16}=\frac{60-4\sqrt{233}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+4\sqrt{233}}{2*16}=\frac{60+4\sqrt{233}}{32}
$