1/4x-8=2x+4

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

1/4x-8=2x+4

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

-8x^2-16x-32x+1=0

We add all the numbers together, and all the variables

-8x^2-48x+1=0

a = -8; b = -48; c = +1;
Δ = b2-4ac
Δ = -482-4·(-8)·1
Δ = 2336
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:

$\sqrt{\Delta}=\sqrt{2336}=\sqrt{16*146}=\sqrt{16}*\sqrt{146}=4\sqrt{146}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-4\sqrt{146}}{2*-8}=\frac{48-4\sqrt{146}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+4\sqrt{146}}{2*-8}=\frac{48+4\sqrt{146}}{-16}
$