2x+5/x=50

Solution for 2x+5/x=50 equation:

2x+5/x=50

We move all terms to the left:

2x+5/x-(50)=0


Domain of the equation: x!=0

x∈R


We multiply all the terms by the denominator


2x*x-50*x+5=0

We add all the numbers together, and all the variables

-50x+2x*x+5=0

Wy multiply elements

2x^2-50x+5=0

a = 2; b = -50; c = +5;
Δ = b2-4ac
Δ = -502-4·2·5
Δ = 2460
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:

$\sqrt{\Delta}=\sqrt{2460}=\sqrt{4*615}=\sqrt{4}*\sqrt{615}=2\sqrt{615}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-2\sqrt{615}}{2*2}=\frac{50-2\sqrt{615}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+2\sqrt{615}}{2*2}=\frac{50+2\sqrt{615}}{4}
$