6(x/2-1)=6(2/3x-3)

Solution for 6(x/2-1)=6(2/3x-3) equation:

6(x/2-1)=6(2/3x-3)

We move all terms to the left:

6(x/2-1)-(6(2/3x-3))=0


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

x∈R


We multiply parentheses

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

6x*3x-6*3x-3))-(6(-1))=0

We add all the numbers together, and all the variables

6x*3x-6*3x=0

Wy multiply elements

18x^2-18x=0

a = 18; b = -18; c = 0;
Δ = b2-4ac
Δ = -182-4·18·0
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-18}{2*18}=\frac{0}{36}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+18}{2*18}=\frac{36}{36}
=1
$