/4x+2=2x+6

Solution for /4x+2=2x+6 equation:

/4x+2=2x+6

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We get rid of parentheses

/4x-2x-6+2=0

We multiply all the terms by the denominator


-2x*4x-6*4x+2*4x+=0

We add all the numbers together, and all the variables

-2x*4x-6*4x+2*4x=0

Wy multiply elements

-8x^2-24x+8x=0

We add all the numbers together, and all the variables

-8x^2-16x=0

a = -8; b = -16; c = 0;
Δ = b2-4ac
Δ = -162-4·(-8)·0
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-16}{2*-8}=\frac{0}{-16}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+16}{2*-8}=\frac{32}{-16}
=-2
$