1/4x=12-x

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

1/4x=12-x

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

1/4x+1x-12=0

We multiply all the terms by the denominator


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

Wy multiply elements

4x^2-48x+1=0

a = 4; b = -48; c = +1;
Δ = b2-4ac
Δ = -482-4·4·1
Δ = 2288
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:

$\sqrt{\Delta}=\sqrt{2288}=\sqrt{16*143}=\sqrt{16}*\sqrt{143}=4\sqrt{143}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-4\sqrt{143}}{2*4}=\frac{48-4\sqrt{143}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+4\sqrt{143}}{2*4}=\frac{48+4\sqrt{143}}{8}
$