3(x-2)+7x=(1/2)(6x-2)

Solution for 3(x-2)+7x=(1/2)(6x-2) equation:

3(x-2)+7x=(1/2)(6x-2)

We move all terms to the left:

3(x-2)+7x-((1/2)(6x-2))=0


Domain of the equation: 2)(6x-2))!=0

x∈R


We add all the numbers together, and all the variables

3(x-2)+7x-((+1/2)(6x-2))=0

We add all the numbers together, and all the variables

7x+3(x-2)-((+1/2)(6x-2))=0

We multiply parentheses

7x+3x-((+1/2)(6x-2))-6=0

We multiply parentheses ..

-((+6x^2+1/2*-2))+7x+3x-6=0

We multiply all the terms by the denominator


-((+6x^2+1+7x*2*-2))+3x*2*-2))-6*2*-2))=0


We calculate terms in parentheses: -((+6x^2+1+7x*2*-2)), so:

(+6x^2+1+7x*2*-2)

We get rid of parentheses

6x^2+7x*2*+1-2

We add all the numbers together, and all the variables

6x^2+7x*2*-1

Wy multiply elements

6x^2+14x^2-1

We add all the numbers together, and all the variables

20x^2-1

Back to the equation:

-(20x^2-1)


We add all the numbers together, and all the variables

-(20x^2-1)+3x*2*=0

Wy multiply elements

6x^2-(20x^2-1)=0

We get rid of parentheses

6x^2-20x^2+1=0

We add all the numbers together, and all the variables

-14x^2+1=0

a = -14; b = 0; c = +1;
Δ = b2-4ac
Δ = 02-4·(-14)·1
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*-14}=\frac{0-2\sqrt{14}}{-28}
=-\frac{2\sqrt{14}}{-28}
=-\frac{\sqrt{14}}{-14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{14}}{2*-14}=\frac{0+2\sqrt{14}}{-28}
=\frac{2\sqrt{14}}{-28}
=\frac{\sqrt{14}}{-14}
$