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

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

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

We move all terms to the left:

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


Domain of the equation: 4x+1))!=0

x∈R


We calculate fractions


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

Fractions to decimals

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

We multiply all the terms by the denominator


2x*4x+1*4x+()=0

We add all the numbers together, and all the variables

2x*4x+1*4x=0

Wy multiply elements

8x^2+4x=0

a = 8; b = 4; c = 0;
Δ = b2-4ac
Δ = 42-4·8·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4}{2*8}=\frac{-8}{16}
=-1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4}{2*8}=\frac{0}{16}
=0
$