3(x-9)(x-2)-(x-7)(x-9)=0

Solution for 3(x-9)(x-2)-(x-7)(x-9)=0 equation:

3(x-9)(x-2)-(x-7)(x-9)=0

We multiply parentheses ..

3(+x^2-2x-9x+18)-(x-7)(x-9)=0

We multiply parentheses

3x^2-6x-27x-(x-7)(x-9)+54=0

We multiply parentheses ..

3x^2-(+x^2-9x-7x+63)-6x-27x+54=0

We add all the numbers together, and all the variables

3x^2-(+x^2-9x-7x+63)-33x+54=0

We get rid of parentheses

3x^2-x^2+9x+7x-33x-63+54=0

We add all the numbers together, and all the variables

2x^2-17x-9=0

a = 2; b = -17; c = -9;
Δ = b2-4ac
Δ = -172-4·2·(-9)
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-17)-19}{2*2}=\frac{-2}{4}
=-1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+19}{2*2}=\frac{36}{4}
=9
$