16-4x=-1/4*16x+64

Solution for 16-4x=-1/4*16x+64 equation:

16-4x=-1/4*16x+64

We move all terms to the left:

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


Domain of the equation: 4*16x+64)!=0

x∈R


We get rid of parentheses

-4x+1/4*16x-64+16=0

We multiply all the terms by the denominator


-4x*4*16x-64*4*16x+16*4*16x+1=0

Wy multiply elements

-256x^2*1-4096x*1+1024x*1+1=0

Wy multiply elements

-256x^2-4096x+1024x+1=0

We add all the numbers together, and all the variables

-256x^2-3072x+1=0

a = -256; b = -3072; c = +1;
Δ = b2-4ac
Δ = -30722-4·(-256)·1
Δ = 9438208
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:

$\sqrt{\Delta}=\sqrt{9438208}=\sqrt{1024*9217}=\sqrt{1024}*\sqrt{9217}=32\sqrt{9217}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3072)-32\sqrt{9217}}{2*-256}=\frac{3072-32\sqrt{9217}}{-512}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3072)+32\sqrt{9217}}{2*-256}=\frac{3072+32\sqrt{9217}}{-512}
$