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

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

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

We move all terms to the left:

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


Domain of the equation: 4)(8-64x))!=0

x∈R


We add all the numbers together, and all the variables

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

We multiply parentheses

-16x-((+1/4)(-64x+8))+2=0

We multiply parentheses ..

-((-64x^2+1/4*8))-16x+2=0

We multiply all the terms by the denominator


-((-64x^2+1-16x*4*8))+2*4*8))=0


We calculate terms in parentheses: -((-64x^2+1-16x*4*8)), so:

(-64x^2+1-16x*4*8)

We get rid of parentheses

-64x^2-16x*4*8+1

Wy multiply elements

-64x^2-512x*8+1

Wy multiply elements

-64x^2-4096x+1

Back to the equation:

-(-64x^2-4096x+1)


We add all the numbers together, and all the variables

-(-64x^2-4096x+1)=0

We get rid of parentheses

64x^2+4096x-1=0

a = 64; b = 4096; c = -1;
Δ = b2-4ac
Δ = 40962-4·64·(-1)
Δ = 16777472
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:

$\sqrt{\Delta}=\sqrt{16777472}=\sqrt{256*65537}=\sqrt{256}*\sqrt{65537}=16\sqrt{65537}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4096)-16\sqrt{65537}}{2*64}=\frac{-4096-16\sqrt{65537}}{128}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4096)+16\sqrt{65537}}{2*64}=\frac{-4096+16\sqrt{65537}}{128}
$