0=t^2-24t-81

Solution for 0=t^2-24t-81 equation:

0=t^2-24t-81

We move all terms to the left:

0-(t^2-24t-81)=0

We add all the numbers together, and all the variables

-(t^2-24t-81)=0

We get rid of parentheses

-t^2+24t+81=0

We add all the numbers together, and all the variables

-1t^2+24t+81=0

a = -1; b = 24; c = +81;
Δ = b2-4ac
Δ = 242-4·(-1)·81
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-30}{2*-1}=\frac{-54}{-2}
=+27
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+30}{2*-1}=\frac{6}{-2}
=-3
$