40=-16t^2+60t+1

Solution for 40=-16t^2+60t+1 equation:

40=-16t^2+60t+1

We move all terms to the left:

40-(-16t^2+60t+1)=0

We get rid of parentheses

16t^2-60t-1+40=0

We add all the numbers together, and all the variables

16t^2-60t+39=0

a = 16; b = -60; c = +39;
Δ = b2-4ac
Δ = -602-4·16·39
Δ = 1104
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:

$\sqrt{\Delta}=\sqrt{1104}=\sqrt{16*69}=\sqrt{16}*\sqrt{69}=4\sqrt{69}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-4\sqrt{69}}{2*16}=\frac{60-4\sqrt{69}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+4\sqrt{69}}{2*16}=\frac{60+4\sqrt{69}}{32}
$