1/4x-128=x-12

Solution for 1/4x-128=x-12 equation:

1/4x-128=x-12

We move all terms to the left:

1/4x-128-(x-12)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We get rid of parentheses

1/4x-x+12-128=0

We multiply all the terms by the denominator


-x*4x+12*4x-128*4x+1=0

Wy multiply elements

-4x^2+48x-512x+1=0

We add all the numbers together, and all the variables

-4x^2-464x+1=0

a = -4; b = -464; c = +1;
Δ = b2-4ac
Δ = -4642-4·(-4)·1
Δ = 215312
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:

$\sqrt{\Delta}=\sqrt{215312}=\sqrt{16*13457}=\sqrt{16}*\sqrt{13457}=4\sqrt{13457}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-464)-4\sqrt{13457}}{2*-4}=\frac{464-4\sqrt{13457}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-464)+4\sqrt{13457}}{2*-4}=\frac{464+4\sqrt{13457}}{-8}
$