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

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

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

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

Wy multiply elements

-4x^2+8x-32x-2=0

We add all the numbers together, and all the variables

-4x^2-24x-2=0

a = -4; b = -24; c = -2;
Δ = b2-4ac
Δ = -242-4·(-4)·(-2)
Δ = 544
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:

$\sqrt{\Delta}=\sqrt{544}=\sqrt{16*34}=\sqrt{16}*\sqrt{34}=4\sqrt{34}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-4\sqrt{34}}{2*-4}=\frac{24-4\sqrt{34}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+4\sqrt{34}}{2*-4}=\frac{24+4\sqrt{34}}{-8}
$