60/(x-2)=x

Solution for 60/(x-2)=x equation:

60/(x-2)=x

We move all terms to the left:

60/(x-2)-(x)=0


Domain of the equation: (x-2)!=0

We move all terms containing x to the left, all other terms to the right

x!=2

x∈R


We add all the numbers together, and all the variables

-1x+60/(x-2)=0

We multiply all the terms by the denominator


-1x*(x-2)+60=0

We multiply parentheses

-x^2+2x+60=0

We add all the numbers together, and all the variables

-1x^2+2x+60=0

a = -1; b = 2; c = +60;
Δ = b2-4ac
Δ = 22-4·(-1)·60
Δ = 244
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:

$\sqrt{\Delta}=\sqrt{244}=\sqrt{4*61}=\sqrt{4}*\sqrt{61}=2\sqrt{61}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{61}}{2*-1}=\frac{-2-2\sqrt{61}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{61}}{2*-1}=\frac{-2+2\sqrt{61}}{-2}
$