5x(16/5x)=17

Solution for 5x(16/5x)=17 equation:

5x(16/5x)=17

We move all terms to the left:

5x(16/5x)-(17)=0


Domain of the equation: 5x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

5x(+16/5x)-17=0

We multiply parentheses

80x^2-17=0

a = 80; b = 0; c = -17;
Δ = b2-4ac
Δ = 02-4·80·(-17)
Δ = 5440
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:

$\sqrt{\Delta}=\sqrt{5440}=\sqrt{64*85}=\sqrt{64}*\sqrt{85}=8\sqrt{85}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{85}}{2*80}=\frac{0-8\sqrt{85}}{160}
=-\frac{8\sqrt{85}}{160}
=-\frac{\sqrt{85}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{85}}{2*80}=\frac{0+8\sqrt{85}}{160}
=\frac{8\sqrt{85}}{160}
=\frac{\sqrt{85}}{20}
$