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

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

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


Domain of the equation: 3x-6)!=0

x∈R


We multiply parentheses ..

(+2x^2-6x-4x+12)=0

We get rid of parentheses

2x^2-6x-4x+12=0

We add all the numbers together, and all the variables

2x^2-10x+12=0

a = 2; b = -10; c = +12;
Δ = b2-4ac
Δ = -102-4·2·12
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2}{2*2}=\frac{8}{4}
=2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2}{2*2}=\frac{12}{4}
=3
$