-2x=1/2x+8

Solution for -2x=1/2x+8 equation:

-2x=1/2x+8

We move all terms to the left:

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


Domain of the equation: 2x+8)!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

a = -4; b = -16; c = -1;
Δ = b2-4ac
Δ = -162-4·(-4)·(-1)
Δ = 240
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:

$\sqrt{\Delta}=\sqrt{240}=\sqrt{16*15}=\sqrt{16}*\sqrt{15}=4\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-4\sqrt{15}}{2*-4}=\frac{16-4\sqrt{15}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+4\sqrt{15}}{2*-4}=\frac{16+4\sqrt{15}}{-8}
$