1/4x-64=2x-8

Solution for 1/4x-64=2x-8 equation:

1/4x-64=2x-8

We move all terms to the left:

1/4x-64-(2x-8)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We get rid of parentheses

1/4x-2x+8-64=0

We multiply all the terms by the denominator


-2x*4x+8*4x-64*4x+1=0

Wy multiply elements

-8x^2+32x-256x+1=0

We add all the numbers together, and all the variables

-8x^2-224x+1=0

a = -8; b = -224; c = +1;
Δ = b2-4ac
Δ = -2242-4·(-8)·1
Δ = 50208
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:

$\sqrt{\Delta}=\sqrt{50208}=\sqrt{16*3138}=\sqrt{16}*\sqrt{3138}=4\sqrt{3138}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-224)-4\sqrt{3138}}{2*-8}=\frac{224-4\sqrt{3138}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-224)+4\sqrt{3138}}{2*-8}=\frac{224+4\sqrt{3138}}{-16}
$