2x+16=2/5x

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

2x+16=2/5x

We move all terms to the left:

2x+16-(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

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

We get rid of parentheses

2x-2/5x+16=0

We multiply all the terms by the denominator


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

Wy multiply elements

10x^2+80x-2=0

a = 10; b = 80; c = -2;
Δ = b2-4ac
Δ = 802-4·10·(-2)
Δ = 6480
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:

$\sqrt{\Delta}=\sqrt{6480}=\sqrt{1296*5}=\sqrt{1296}*\sqrt{5}=36\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(80)-36\sqrt{5}}{2*10}=\frac{-80-36\sqrt{5}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(80)+36\sqrt{5}}{2*10}=\frac{-80+36\sqrt{5}}{20}
$