(2/5*x)10=16

Solution for (2/5*x)10=16 equation:

(2/5*x)10=16

We move all terms to the left:

(2/5*x)10-(16)=0


Domain of the equation: 5*x)10!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+2/5*x)10-16=0

We multiply parentheses

20x^2-16=0

a = 20; b = 0; c = -16;
Δ = b2-4ac
Δ = 02-4·20·(-16)
Δ = 1280
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:

$\sqrt{\Delta}=\sqrt{1280}=\sqrt{256*5}=\sqrt{256}*\sqrt{5}=16\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-16\sqrt{5}}{2*20}=\frac{0-16\sqrt{5}}{40}
=-\frac{16\sqrt{5}}{40}
=-\frac{2\sqrt{5}}{5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+16\sqrt{5}}{2*20}=\frac{0+16\sqrt{5}}{40}
=\frac{16\sqrt{5}}{40}
=\frac{2\sqrt{5}}{5}
$