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

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

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

We move all terms to the left:

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


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

x∈R


We add all the numbers together, and all the variables

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

We multiply parentheses ..

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

We multiply all the terms by the denominator


-((+4x^2+1+x*2*2))+7*2*2))=0


We calculate terms in parentheses: -((+4x^2+1+x*2*2)), so:

(+4x^2+1+x*2*2)

We get rid of parentheses

4x^2+x*2*2+1

Wy multiply elements

4x^2+4x*2+1

Wy multiply elements

4x^2+8x+1

Back to the equation:

-(4x^2+8x+1)


We add all the numbers together, and all the variables

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

We get rid of parentheses

-4x^2-8x-1=0

a = -4; b = -8; c = -1;
Δ = b2-4ac
Δ = -82-4·(-4)·(-1)
Δ = 48
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:

$\sqrt{\Delta}=\sqrt{48}=\sqrt{16*3}=\sqrt{16}*\sqrt{3}=4\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{3}}{2*-4}=\frac{8-4\sqrt{3}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{3}}{2*-4}=\frac{8+4\sqrt{3}}{-8}
$