65/x+2x=130

Solution for 65/x+2x=130 equation:

65/x+2x=130

We move all terms to the left:

65/x+2x-(130)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

2x+65/x-130=0

We multiply all the terms by the denominator


2x*x-130*x+65=0

We add all the numbers together, and all the variables

-130x+2x*x+65=0

Wy multiply elements

2x^2-130x+65=0

a = 2; b = -130; c = +65;
Δ = b2-4ac
Δ = -1302-4·2·65
Δ = 16380
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:

$\sqrt{\Delta}=\sqrt{16380}=\sqrt{36*455}=\sqrt{36}*\sqrt{455}=6\sqrt{455}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-130)-6\sqrt{455}}{2*2}=\frac{130-6\sqrt{455}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-130)+6\sqrt{455}}{2*2}=\frac{130+6\sqrt{455}}{4}
$