52=-16t^2+60t+16

Solution for 52=-16t^2+60t+16 equation:

52=-16t^2+60t+16

We move all terms to the left:

52-(-16t^2+60t+16)=0

We get rid of parentheses

16t^2-60t-16+52=0

We add all the numbers together, and all the variables

16t^2-60t+36=0

a = 16; b = -60; c = +36;
Δ = b2-4ac
Δ = -602-4·16·36
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-36}{2*16}=\frac{24}{32}
=3/4
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+36}{2*16}=\frac{96}{32}
=3
$