0.2x+0.4x-2=-2/5x

Solution for 0.2x+0.4x-2=-2/5x equation:

0.2x+0.4x-2=-2/5x

We move all terms to the left:

0.2x+0.4x-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

0.6x-(-2/5x)-2=0

We get rid of parentheses

0.6x+2/5x-2=0

We multiply all the terms by the denominator


(0.6x)*5x-2*5x+2=0

We add all the numbers together, and all the variables

(+0.6x)*5x-2*5x+2=0

We multiply parentheses

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

Wy multiply elements

0x^2-10x+2=0

We add all the numbers together, and all the variables

x^2-10x+2=0

a = 1; b = -10; c = +2;
Δ = b2-4ac
Δ = -102-4·1·2
Δ = 92
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:

$\sqrt{\Delta}=\sqrt{92}=\sqrt{4*23}=\sqrt{4}*\sqrt{23}=2\sqrt{23}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{23}}{2*1}=\frac{10-2\sqrt{23}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{23}}{2*1}=\frac{10+2\sqrt{23}}{2}
$