t^2-81=121

Solution for t^2-81=121 equation:

t^2-81=121

We move all terms to the left:

t^2-81-(121)=0

We add all the numbers together, and all the variables

t^2-202=0

a = 1; b = 0; c = -202;
Δ = b2-4ac
Δ = 02-4·1·(-202)
Δ = 808
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:

$\sqrt{\Delta}=\sqrt{808}=\sqrt{4*202}=\sqrt{4}*\sqrt{202}=2\sqrt{202}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{202}}{2*1}=\frac{0-2\sqrt{202}}{2}
=-\frac{2\sqrt{202}}{2}
=-\sqrt{202}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{202}}{2*1}=\frac{0+2\sqrt{202}}{2}
=\frac{2\sqrt{202}}{2}
=\sqrt{202}
$