x/3x+8-x=-4x-6

Solution for x/3x+8-x=-4x-6 equation:

x/3x+8-x=-4x-6

We move all terms to the left:

x/3x+8-x-(-4x-6)=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+x/3x-(-4x-6)+8=0

We get rid of parentheses

-1x+x/3x+4x+6+8=0

We multiply all the terms by the denominator


-1x*3x+x+4x*3x+6*3x+8*3x=0

We add all the numbers together, and all the variables

x-1x*3x+4x*3x+6*3x+8*3x=0

Wy multiply elements

-3x^2+12x^2+x+18x+24x=0

We add all the numbers together, and all the variables

9x^2+43x=0

a = 9; b = 43; c = 0;
Δ = b2-4ac
Δ = 432-4·9·0
Δ = 1849
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1849}=43$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(43)-43}{2*9}=\frac{-86}{18}
=-4+7/9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(43)+43}{2*9}=\frac{0}{18}
=0
$