t(t-1)=11

Solution for t(t-1)=11 equation:

t(t-1)=11

We move all terms to the left:

t(t-1)-(11)=0

We multiply parentheses

t^2-1t-11=0

a = 1; b = -1; c = -11;
Δ = b2-4ac
Δ = -12-4·1·(-11)
Δ = 45
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:

$\sqrt{\Delta}=\sqrt{45}=\sqrt{9*5}=\sqrt{9}*\sqrt{5}=3\sqrt{5}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-3\sqrt{5}}{2*1}=\frac{1-3\sqrt{5}}{2}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+3\sqrt{5}}{2*1}=\frac{1+3\sqrt{5}}{2}
$