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

Solution for X-((1/2)*(4x+2))=0 equation:

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))=0

We multiply parentheses ..

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

We multiply all the terms by the denominator


-((+4X^2+1+X*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 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}
$