(3x-2)(x-3)-6=0

Solution for (3x-2)(x-3)-6=0 equation:

(3x-2)(x-3)-6=0

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

3x^2-11x=0

a = 3; b = -11; c = 0;
Δ = b2-4ac
Δ = -112-4·3·0
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-11}{2*3}=\frac{0}{6}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+11}{2*3}=\frac{22}{6}
=3+2/3
$