3x^2-9x-165=0

Solution for 3x^2-9x-165=0 equation:

3x^2-9x-165=0

a = 3; b = -9; c = -165;
Δ = b2-4ac
Δ = -92-4·3·(-165)
Δ = 2061
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:

$\sqrt{\Delta}=\sqrt{2061}=\sqrt{9*229}=\sqrt{9}*\sqrt{229}=3\sqrt{229}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-3\sqrt{229}}{2*3}=\frac{9-3\sqrt{229}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+3\sqrt{229}}{2*3}=\frac{9+3\sqrt{229}}{6}
$