t(t+1)=64

Solution for t(t+1)=64 equation:

t(t+1)=64

We move all terms to the left:

t(t+1)-(64)=0

We multiply parentheses

t^2+t-64=0

a = 1; b = 1; c = -64;
Δ = b2-4ac
Δ = 12-4·1·(-64)
Δ = 257
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{257}}{2*1}=\frac{-1-\sqrt{257}}{2}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{257}}{2*1}=\frac{-1+\sqrt{257}}{2}
$