11=12t^2-13

Solution for 11=12t^2-13 equation:

11=12t^2-13

We move all terms to the left:

11-(12t^2-13)=0

We get rid of parentheses

-12t^2+13+11=0

We add all the numbers together, and all the variables

-12t^2+24=0

a = -12; b = 0; c = +24;
Δ = b2-4ac
Δ = 02-4·(-12)·24
Δ = 1152
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:

$\sqrt{\Delta}=\sqrt{1152}=\sqrt{576*2}=\sqrt{576}*\sqrt{2}=24\sqrt{2}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-24\sqrt{2}}{2*-12}=\frac{0-24\sqrt{2}}{-24}
=-\frac{24\sqrt{2}}{-24}
=-\frac{\sqrt{2}}{-1}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+24\sqrt{2}}{2*-12}=\frac{0+24\sqrt{2}}{-24}
=\frac{24\sqrt{2}}{-24}
=\frac{\sqrt{2}}{-1}
$