(2/5x+4)*2=2/5x

Solution for (2/5x+4)*2=2/5x equation:

(2/5x+4)*2=2/5x

We move all terms to the left:

(2/5x+4)*2-(2/5x)=0


Domain of the equation: 5x+4)*2!=0

x∈R



Domain of the equation: 5x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(2/5x+4)*2-(+2/5x)=0

We multiply parentheses

4x-(+2/5x)+8=0

We get rid of parentheses

4x-2/5x+8=0

We multiply all the terms by the denominator


4x*5x+8*5x-2=0

Wy multiply elements

20x^2+40x-2=0

a = 20; b = 40; c = -2;
Δ = b2-4ac
Δ = 402-4·20·(-2)
Δ = 1760
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:

$\sqrt{\Delta}=\sqrt{1760}=\sqrt{16*110}=\sqrt{16}*\sqrt{110}=4\sqrt{110}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-4\sqrt{110}}{2*20}=\frac{-40-4\sqrt{110}}{40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+4\sqrt{110}}{2*20}=\frac{-40+4\sqrt{110}}{40}
$