16x=11/5x=1

Solution for 16x=11/5x=1 equation:

16x=11/5x=1

We move all terms to the left:

16x-(11/5x)=0


Domain of the equation: 5x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

16x-(+11/5x)=0

We get rid of parentheses

16x-11/5x=0

We multiply all the terms by the denominator


16x*5x-11=0

Wy multiply elements

80x^2-11=0

a = 80; b = 0; c = -11;
Δ = b2-4ac
Δ = 02-4·80·(-11)
Δ = 3520
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:

$\sqrt{\Delta}=\sqrt{3520}=\sqrt{64*55}=\sqrt{64}*\sqrt{55}=8\sqrt{55}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{55}}{2*80}=\frac{0-8\sqrt{55}}{160}
=-\frac{8\sqrt{55}}{160}
=-\frac{\sqrt{55}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{55}}{2*80}=\frac{0+8\sqrt{55}}{160}
=\frac{8\sqrt{55}}{160}
=\frac{\sqrt{55}}{20}
$