16x=2+2/5x

Solution for 16x=2+2/5x equation:

16x=2+2/5x

We move all terms to the left:

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

We get rid of parentheses

16x-2/5x-2=0

We multiply all the terms by the denominator


16x*5x-2*5x-2=0

Wy multiply elements

80x^2-10x-2=0

a = 80; b = -10; c = -2;
Δ = b2-4ac
Δ = -102-4·80·(-2)
Δ = 740
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:

$\sqrt{\Delta}=\sqrt{740}=\sqrt{4*185}=\sqrt{4}*\sqrt{185}=2\sqrt{185}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{185}}{2*80}=\frac{10-2\sqrt{185}}{160}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{185}}{2*80}=\frac{10+2\sqrt{185}}{160}
$