0,4x+2=-6/5x+x

Solution for 0,4x+2=-6/5x+x equation:

0.4x+2=-6/5x+x

We move all terms to the left:

0.4x+2-(-6/5x+x)=0


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

x∈R


We add all the numbers together, and all the variables

0.4x-(+x-6/5x)+2=0

We get rid of parentheses

0.4x-x+6/5x+2=0

We multiply all the terms by the denominator


(0.4x)*5x-x*5x+2*5x+6=0

We add all the numbers together, and all the variables

(+0.4x)*5x-x*5x+2*5x+6=0

We multiply parentheses

0x^2-x*5x+2*5x+6=0

Wy multiply elements

0x^2-5x^2+10x+6=0

We add all the numbers together, and all the variables

-4x^2+10x+6=0

a = -4; b = 10; c = +6;
Δ = b2-4ac
Δ = 102-4·(-4)·6
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-14}{2*-4}=\frac{-24}{-8}
=+3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+14}{2*-4}=\frac{4}{-8}
=-1/2
$