5/x=x-12

Solution for 5/x=x-12 equation:

5/x=x-12

We move all terms to the left:

5/x-(x-12)=0


Domain of the equation: x!=0

x∈R


We get rid of parentheses

5/x-x+12=0

We multiply all the terms by the denominator


-x*x+12*x+5=0

We add all the numbers together, and all the variables

12x-x*x+5=0

Wy multiply elements

-1x^2+12x+5=0

a = -1; b = 12; c = +5;
Δ = b2-4ac
Δ = 122-4·(-1)·5
Δ = 164
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:

$\sqrt{\Delta}=\sqrt{164}=\sqrt{4*41}=\sqrt{4}*\sqrt{41}=2\sqrt{41}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-2\sqrt{41}}{2*-1}=\frac{-12-2\sqrt{41}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+2\sqrt{41}}{2*-1}=\frac{-12+2\sqrt{41}}{-2}
$