7/6x+8=2/3x-4

Solution for 7/6x+8=2/3x-4 equation:

7/6x+8=2/3x-4

We move all terms to the left:

7/6x+8-(2/3x-4)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R



Domain of the equation: 3x-4)!=0

x∈R


We get rid of parentheses

7/6x-2/3x+4+8=0

We calculate fractions


21x/18x^2+(-12x)/18x^2+4+8=0

We add all the numbers together, and all the variables

21x/18x^2+(-12x)/18x^2+12=0

We multiply all the terms by the denominator


21x+(-12x)+12*18x^2=0

Wy multiply elements

216x^2+21x+(-12x)=0

We get rid of parentheses

216x^2+21x-12x=0

We add all the numbers together, and all the variables

216x^2+9x=0

a = 216; b = 9; c = 0;
Δ = b2-4ac
Δ = 92-4·216·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-9}{2*216}=\frac{-18}{432}
=-1/24
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+9}{2*216}=\frac{0}{432}
=0
$