-1/2x-8=x-4

Solution for -1/2x-8=x-4 equation:

-1/2x-8=x-4

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


-x*2x+4*2x-8*2x-1=0

Wy multiply elements

-2x^2+8x-16x-1=0

We add all the numbers together, and all the variables

-2x^2-8x-1=0

a = -2; b = -8; c = -1;
Δ = b2-4ac
Δ = -82-4·(-2)·(-1)
Δ = 56
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:

$\sqrt{\Delta}=\sqrt{56}=\sqrt{4*14}=\sqrt{4}*\sqrt{14}=2\sqrt{14}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{14}}{2*-2}=\frac{8-2\sqrt{14}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{14}}{2*-2}=\frac{8+2\sqrt{14}}{-4}
$