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

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

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

(-9x^2+3x+18x-6)=0

We get rid of parentheses

-9x^2+3x+18x-6=0

We add all the numbers together, and all the variables

-9x^2+21x-6=0

a = -9; b = 21; c = -6;
Δ = b2-4ac
Δ = 212-4·(-9)·(-6)
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-15}{2*-9}=\frac{-36}{-18}
=+2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+15}{2*-9}=\frac{-6}{-18}
=1/3
$