2x+16=2x/5x

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

2x+16=2x/5x

We move all terms to the left:

2x+16-(2x/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

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

Wy multiply elements

10x^2-2x+80x=0

We add all the numbers together, and all the variables

10x^2+78x=0

a = 10; b = 78; c = 0;
Δ = b2-4ac
Δ = 782-4·10·0
Δ = 6084
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6084}=78$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(78)-78}{2*10}=\frac{-156}{20}
=-7+4/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(78)+78}{2*10}=\frac{0}{20}
=0
$