588/x=x-2

Solution for 588/x=x-2 equation:

588/x=x-2

We move all terms to the left:

588/x-(x-2)=0


Domain of the equation: x!=0

x∈R


We get rid of parentheses

588/x-x+2=0

We multiply all the terms by the denominator


-x*x+2*x+588=0

We add all the numbers together, and all the variables

2x-x*x+588=0

Wy multiply elements

-1x^2+2x+588=0

a = -1; b = 2; c = +588;
Δ = b2-4ac
Δ = 22-4·(-1)·588
Δ = 2356
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:

$\sqrt{\Delta}=\sqrt{2356}=\sqrt{4*589}=\sqrt{4}*\sqrt{589}=2\sqrt{589}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{589}}{2*-1}=\frac{-2-2\sqrt{589}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{589}}{2*-1}=\frac{-2+2\sqrt{589}}{-2}
$