10+x=5)1/5x+2)

Solution for 10+x=5)1/5x+2) equation:

10+x=5)1/5x+2)

We move all terms to the left:

10+x-(5)1/5x+2))=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

x-51/5x=0

We multiply all the terms by the denominator


x*5x-51=0

Wy multiply elements

5x^2-51=0

a = 5; b = 0; c = -51;
Δ = b2-4ac
Δ = 02-4·5·(-51)
Δ = 1020
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:

$\sqrt{\Delta}=\sqrt{1020}=\sqrt{4*255}=\sqrt{4}*\sqrt{255}=2\sqrt{255}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{255}}{2*5}=\frac{0-2\sqrt{255}}{10}
=-\frac{2\sqrt{255}}{10}
=-\frac{\sqrt{255}}{5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{255}}{2*5}=\frac{0+2\sqrt{255}}{10}
=\frac{2\sqrt{255}}{10}
=\frac{\sqrt{255}}{5}
$