-x+1/3x=0.8

Solution for -x+1/3x=0.8 equation:

-x+1/3x=0.8

We move all terms to the left:

-x+1/3x-(0.8)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

-1x+1/3x-0.8=0

We multiply all the terms by the denominator


-1x*3x-(0.8)*3x+1=0

We multiply parentheses

-1x*3x-2.4x+1=0

Wy multiply elements

-3x^2-2.4x+1=0

a = -3; b = -2.4; c = +1;
Δ = b2-4ac
Δ = -2.42-4·(-3)·1
Δ = 17.76
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2.4)-\sqrt{17.76}}{2*-3}=\frac{2.4-\sqrt{17.76}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2.4)+\sqrt{17.76}}{2*-3}=\frac{2.4+\sqrt{17.76}}{-6}
$