7/3*x+5=5/6*x-4

Solution for 7/3*x+5=5/6*x-4 equation:

7/3x+5=5/6x-4

We move all terms to the left:

7/3x+5-(5/6x-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

7/3x-5/6x+4+5=0

We calculate fractions


42x/18x^2+(-15x)/18x^2+4+5=0

We add all the numbers together, and all the variables

42x/18x^2+(-15x)/18x^2+9=0

We multiply all the terms by the denominator


42x+(-15x)+9*18x^2=0

Wy multiply elements

162x^2+42x+(-15x)=0

We get rid of parentheses

162x^2+42x-15x=0

We add all the numbers together, and all the variables

162x^2+27x=0

a = 162; b = 27; c = 0;
Δ = b2-4ac
Δ = 272-4·162·0
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*162}=\frac{-54}{324}
=-1/6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+27}{2*162}=\frac{0}{324}
=0
$