x^2-27x-162=0

Solution for x^2-27x-162=0 equation:

x^2-27x-162=0

a = 1; b = -27; c = -162;
Δ = b2-4ac
Δ = -272-4·1·(-162)
Δ = 1377
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:

$\sqrt{\Delta}=\sqrt{1377}=\sqrt{81*17}=\sqrt{81}*\sqrt{17}=9\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-9\sqrt{17}}{2*1}=\frac{27-9\sqrt{17}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+9\sqrt{17}}{2*1}=\frac{27+9\sqrt{17}}{2}
$