2/x=x-50

Solution for 2/x=x-50 equation:

2/x=x-50

We move all terms to the left:

2/x-(x-50)=0


Domain of the equation: x!=0

x∈R


We get rid of parentheses

2/x-x+50=0

We multiply all the terms by the denominator


-x*x+50*x+2=0

We add all the numbers together, and all the variables

50x-x*x+2=0

Wy multiply elements

-1x^2+50x+2=0

a = -1; b = 50; c = +2;
Δ = b2-4ac
Δ = 502-4·(-1)·2
Δ = 2508
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:

$\sqrt{\Delta}=\sqrt{2508}=\sqrt{4*627}=\sqrt{4}*\sqrt{627}=2\sqrt{627}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(50)-2\sqrt{627}}{2*-1}=\frac{-50-2\sqrt{627}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(50)+2\sqrt{627}}{2*-1}=\frac{-50+2\sqrt{627}}{-2}
$