x(3x-9)=162

Solution for x(3x-9)=162 equation:

x(3x-9)=162

We move all terms to the left:

x(3x-9)-(162)=0

We multiply parentheses

3x^2-9x-162=0

a = 3; b = -9; c = -162;
Δ = b2-4ac
Δ = -92-4·3·(-162)
Δ = 2025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2025}=45$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-45}{2*3}=\frac{-36}{6}
=-6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+45}{2*3}=\frac{54}{6}
=9
$