1/4x-2=4x+8

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

1/4x-2=4x+8

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We add all the numbers together, and all the variables

-16x^2-40x+1=0

a = -16; b = -40; c = +1;
Δ = b2-4ac
Δ = -402-4·(-16)·1
Δ = 1664
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:

$\sqrt{\Delta}=\sqrt{1664}=\sqrt{64*26}=\sqrt{64}*\sqrt{26}=8\sqrt{26}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-8\sqrt{26}}{2*-16}=\frac{40-8\sqrt{26}}{-32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+8\sqrt{26}}{2*-16}=\frac{40+8\sqrt{26}}{-32}
$