(x-6)(x-3)=162

Solution for (x-6)(x-3)=162 equation:

(x-6)(x-3)=162

We move all terms to the left:

(x-6)(x-3)-(162)=0

We multiply parentheses ..

(+x^2-3x-6x+18)-162=0

We get rid of parentheses

x^2-3x-6x+18-162=0

We add all the numbers together, and all the variables

x^2-9x-144=0

a = 1; b = -9; c = -144;
Δ = b2-4ac
Δ = -92-4·1·(-144)
Δ = 657
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:

$\sqrt{\Delta}=\sqrt{657}=\sqrt{9*73}=\sqrt{9}*\sqrt{73}=3\sqrt{73}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-3\sqrt{73}}{2*1}=\frac{9-3\sqrt{73}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+3\sqrt{73}}{2*1}=\frac{9+3\sqrt{73}}{2}
$