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

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

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

We move all terms to the left:

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


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

x∈R


We add all the numbers together, and all the variables

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

We multiply parentheses

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

We multiply parentheses ..

-((+x^2+1/3*-3))+2x-2=0

We multiply all the terms by the denominator


-((+x^2+1+2x*3*-3))-2*3*-3))=0


We calculate terms in parentheses: -((+x^2+1+2x*3*-3)), so:

(+x^2+1+2x*3*-3)

We get rid of parentheses

x^2+2x*3*+1-3

We add all the numbers together, and all the variables

x^2+2x*3*-2

Wy multiply elements

x^2+6x^2-2

We add all the numbers together, and all the variables

7x^2-2

Back to the equation:

-(7x^2-2)


We add all the numbers together, and all the variables

-(7x^2-2)=0

We get rid of parentheses

-7x^2+2=0

a = -7; b = 0; c = +2;
Δ = b2-4ac
Δ = 02-4·(-7)·2
Δ = 56
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{56}=\sqrt{4*14}=\sqrt{4}*\sqrt{14}=2\sqrt{14}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{14}}{2*-7}=\frac{0-2\sqrt{14}}{-14}
=-\frac{2\sqrt{14}}{-14}
=-\frac{\sqrt{14}}{-7}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{14}}{2*-7}=\frac{0+2\sqrt{14}}{-14}
=\frac{2\sqrt{14}}{-14}
=\frac{\sqrt{14}}{-7}
$