(1/2)(6x+8)=2x+4+x

Solution for (1/2)(6x+8)=2x+4+x equation:

(1/2)(6x+8)=2x+4+x

We move all terms to the left:

(1/2)(6x+8)-(2x+4+x)=0


Domain of the equation: 2)(6x+8)!=0

x∈R


We add all the numbers together, and all the variables

(+1/2)(6x+8)-(3x+4)=0

We get rid of parentheses

(+1/2)(6x+8)-3x-4=0

We multiply parentheses ..

(+6x^2+1/2*8)-3x-4=0

We multiply all the terms by the denominator


(+6x^2+1-3x*2*8)-4*2*8)=0

We add all the numbers together, and all the variables

(+6x^2+1-3x*2*8)=0

We get rid of parentheses

6x^2-3x*2*8+1=0

Wy multiply elements

6x^2-48x*8+1=0

Wy multiply elements

6x^2-384x+1=0

a = 6; b = -384; c = +1;
Δ = b2-4ac
Δ = -3842-4·6·1
Δ = 147432
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:

$\sqrt{\Delta}=\sqrt{147432}=\sqrt{4*36858}=\sqrt{4}*\sqrt{36858}=2\sqrt{36858}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-384)-2\sqrt{36858}}{2*6}=\frac{384-2\sqrt{36858}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-384)+2\sqrt{36858}}{2*6}=\frac{384+2\sqrt{36858}}{12}
$