4x=1/2x-4

Solution for 4x=1/2x-4 equation:

4x=1/2x-4

We move all terms to the left:

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


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

x∈R


We get rid of parentheses

4x-1/2x+4=0

We multiply all the terms by the denominator


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

Wy multiply elements

8x^2+8x-1=0

a = 8; b = 8; c = -1;
Δ = b2-4ac
Δ = 82-4·8·(-1)
Δ = 96
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:

$\sqrt{\Delta}=\sqrt{96}=\sqrt{16*6}=\sqrt{16}*\sqrt{6}=4\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-4\sqrt{6}}{2*8}=\frac{-8-4\sqrt{6}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+4\sqrt{6}}{2*8}=\frac{-8+4\sqrt{6}}{16}
$