5x+5/x=52

Solution for 5x+5/x=52 equation:

5x+5/x=52

We move all terms to the left:

5x+5/x-(52)=0


Domain of the equation: x!=0

x∈R


We multiply all the terms by the denominator


5x*x-52*x+5=0

We add all the numbers together, and all the variables

-52x+5x*x+5=0

Wy multiply elements

5x^2-52x+5=0

a = 5; b = -52; c = +5;
Δ = b2-4ac
Δ = -522-4·5·5
Δ = 2604
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:

$\sqrt{\Delta}=\sqrt{2604}=\sqrt{4*651}=\sqrt{4}*\sqrt{651}=2\sqrt{651}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-52)-2\sqrt{651}}{2*5}=\frac{52-2\sqrt{651}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-52)+2\sqrt{651}}{2*5}=\frac{52+2\sqrt{651}}{10}
$