2x+40=2/10x

Solution for 2x+40=2/10x equation:

2x+40=2/10x

We move all terms to the left:

2x+40-(2/10x)=0


Domain of the equation: 10x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

2x-(+2/10x)+40=0

We get rid of parentheses

2x-2/10x+40=0

We multiply all the terms by the denominator


2x*10x+40*10x-2=0

Wy multiply elements

20x^2+400x-2=0

a = 20; b = 400; c = -2;
Δ = b2-4ac
Δ = 4002-4·20·(-2)
Δ = 160160
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:

$\sqrt{\Delta}=\sqrt{160160}=\sqrt{16*10010}=\sqrt{16}*\sqrt{10010}=4\sqrt{10010}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(400)-4\sqrt{10010}}{2*20}=\frac{-400-4\sqrt{10010}}{40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(400)+4\sqrt{10010}}{2*20}=\frac{-400+4\sqrt{10010}}{40}
$