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

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

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

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 6x-4)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


48x/18x^2+(-21x)/18x^2+4+3=0

We add all the numbers together, and all the variables

48x/18x^2+(-21x)/18x^2+7=0

We multiply all the terms by the denominator


48x+(-21x)+7*18x^2=0

Wy multiply elements

126x^2+48x+(-21x)=0

We get rid of parentheses

126x^2+48x-21x=0

We add all the numbers together, and all the variables

126x^2+27x=0

a = 126; b = 27; c = 0;
Δ = b2-4ac
Δ = 272-4·126·0
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-27}{2*126}=\frac{-54}{252}
=-3/14
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+27}{2*126}=\frac{0}{252}
=0
$