-1/3x+3=-0,1x-6

Solution for -1/3x+3=-0,1x-6 equation:

-1/3x+3=-0.1x-6

We move all terms to the left:

-1/3x+3-(-0.1x-6)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

-1/3x+0.1x+6+3=0

We multiply all the terms by the denominator


(0.1x)*3x+6*3x+3*3x-1=0

We add all the numbers together, and all the variables

(+0.1x)*3x+6*3x+3*3x-1=0

We multiply parentheses

0x^2+6*3x+3*3x-1=0

Wy multiply elements

0x^2+18x+9x-1=0

We add all the numbers together, and all the variables

x^2+27x-1=0

a = 1; b = 27; c = -1;
Δ = b2-4ac
Δ = 272-4·1·(-1)
Δ = 733
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{-(27)-\sqrt{733}}{2*1}=\frac{-27-\sqrt{733}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+\sqrt{733}}{2*1}=\frac{-27+\sqrt{733}}{2}
$