2x+1=(1/2)(x-7+4x)

Solution for 2x+1=(1/2)(x-7+4x) equation:

2x+1=(1/2)(x-7+4x)

We move all terms to the left:

2x+1-((1/2)(x-7+4x))=0


Domain of the equation: 2)(x-7+4x))!=0

We move all terms containing x to the left, all other terms to the right

2)(x+4x))!=7

x∈R


We add all the numbers together, and all the variables

2x-((+1/2)(5x-7))+1=0

We multiply parentheses ..

-((+5x^2+1/2*-7))+2x+1=0

We multiply all the terms by the denominator


-((+5x^2+1+2x*2*-7))+1*2*-7))=0


We calculate terms in parentheses: -((+5x^2+1+2x*2*-7)), so:

(+5x^2+1+2x*2*-7)

We get rid of parentheses

5x^2+2x*2*+1-7

We add all the numbers together, and all the variables

5x^2+2x*2*-6

Wy multiply elements

5x^2+4x^2-6

We add all the numbers together, and all the variables

9x^2-6

Back to the equation:

-(9x^2-6)


We add all the numbers together, and all the variables

-(9x^2-6)=0

We get rid of parentheses

-9x^2+6=0

a = -9; b = 0; c = +6;
Δ = b2-4ac
Δ = 02-4·(-9)·6
Δ = 216
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:

$\sqrt{\Delta}=\sqrt{216}=\sqrt{36*6}=\sqrt{36}*\sqrt{6}=6\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{6}}{2*-9}=\frac{0-6\sqrt{6}}{-18}
=-\frac{6\sqrt{6}}{-18}
=-\frac{\sqrt{6}}{-3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{6}}{2*-9}=\frac{0+6\sqrt{6}}{-18}
=\frac{6\sqrt{6}}{-18}
=\frac{\sqrt{6}}{-3}
$