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

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

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

We move all terms to the left:

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


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

x∈R


We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

We multiply parentheses

8x^2-16x+1=0

a = 8; b = -16; c = +1;
Δ = b2-4ac
Δ = -162-4·8·1
Δ = 224
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:

$\sqrt{\Delta}=\sqrt{224}=\sqrt{16*14}=\sqrt{16}*\sqrt{14}=4\sqrt{14}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-4\sqrt{14}}{2*8}=\frac{16-4\sqrt{14}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+4\sqrt{14}}{2*8}=\frac{16+4\sqrt{14}}{16}
$