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

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

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

We move all terms to the left:

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


Domain of the equation: 2x-2)!=0

x∈R


We multiply parentheses

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

We get rid of parentheses

8x-1/2x+2+2=0

We multiply all the terms by the denominator


8x*2x+2*2x+2*2x-1=0

Wy multiply elements

16x^2+4x+4x-1=0

We add all the numbers together, and all the variables

16x^2+8x-1=0

a = 16; b = 8; c = -1;
Δ = b2-4ac
Δ = 82-4·16·(-1)
Δ = 128
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:

$\sqrt{\Delta}=\sqrt{128}=\sqrt{64*2}=\sqrt{64}*\sqrt{2}=8\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-8\sqrt{2}}{2*16}=\frac{-8-8\sqrt{2}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8\sqrt{2}}{2*16}=\frac{-8+8\sqrt{2}}{32}
$