X2-9x-81=0

Solution for X2-9x-81=0 equation:

X2-9X-81=0

We add all the numbers together, and all the variables

X^2-9X-81=0

a = 1; b = -9; c = -81;
Δ = b2-4ac
Δ = -92-4·1·(-81)
Δ = 405
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{405}=\sqrt{81*5}=\sqrt{81}*\sqrt{5}=9\sqrt{5}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-9\sqrt{5}}{2*1}=\frac{9-9\sqrt{5}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+9\sqrt{5}}{2*1}=\frac{9+9\sqrt{5}}{2}
$