4/x=x-12

Solution for 4/x=x-12 equation:

4/x=x-12

We move all terms to the left:

4/x-(x-12)=0


Domain of the equation: x!=0

x∈R


We get rid of parentheses

4/x-x+12=0

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

12x-x*x+4=0

Wy multiply elements

-1x^2+12x+4=0

a = -1; b = 12; c = +4;
Δ = b2-4ac
Δ = 122-4·(-1)·4
Δ = 160
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:

$\sqrt{\Delta}=\sqrt{160}=\sqrt{16*10}=\sqrt{16}*\sqrt{10}=4\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-4\sqrt{10}}{2*-1}=\frac{-12-4\sqrt{10}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+4\sqrt{10}}{2*-1}=\frac{-12+4\sqrt{10}}{-2}
$