5x^2-18x-81=0

Solution for 5x^2-18x-81=0 equation:

5x^2-18x-81=0

a = 5; b = -18; c = -81;
Δ = b2-4ac
Δ = -182-4·5·(-81)
Δ = 1944
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:

$\sqrt{\Delta}=\sqrt{1944}=\sqrt{324*6}=\sqrt{324}*\sqrt{6}=18\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-18\sqrt{6}}{2*5}=\frac{18-18\sqrt{6}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+18\sqrt{6}}{2*5}=\frac{18+18\sqrt{6}}{10}
$