5x+5/x=x+52

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

5X+5/X=X+52

We move all terms to the left:

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


Domain of the equation: X!=0

X∈R


We get rid of parentheses

5X+5/X-X-52=0

We multiply all the terms by the denominator


5X*X-X*X-52*X+5=0

We add all the numbers together, and all the variables

-52X+5X*X-X*X+5=0

Wy multiply elements

5X^2-1X^2-52X+5=0

We add all the numbers together, and all the variables

4X^2-52X+5=0

a = 4; b = -52; c = +5;
Δ = b2-4ac
Δ = -522-4·4·5
Δ = 2624
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:

$\sqrt{\Delta}=\sqrt{2624}=\sqrt{64*41}=\sqrt{64}*\sqrt{41}=8\sqrt{41}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-52)-8\sqrt{41}}{2*4}=\frac{52-8\sqrt{41}}{8}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-52)+8\sqrt{41}}{2*4}=\frac{52+8\sqrt{41}}{8}
$