7/3x+9=6/2x-1

Solution for 7/3x+9=6/2x-1 equation:

7/3x+9=6/2x-1

We move all terms to the left:

7/3x+9-(6/2x-1)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 2x-1)!=0

x∈R


We get rid of parentheses

7/3x-6/2x+1+9=0

We calculate fractions


14x/6x^2+(-18x)/6x^2+1+9=0

We add all the numbers together, and all the variables

14x/6x^2+(-18x)/6x^2+10=0

We multiply all the terms by the denominator


14x+(-18x)+10*6x^2=0

Wy multiply elements

60x^2+14x+(-18x)=0

We get rid of parentheses

60x^2+14x-18x=0

We add all the numbers together, and all the variables

60x^2-4x=0

a = 60; b = -4; c = 0;
Δ = b2-4ac
Δ = -42-4·60·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4}{2*60}=\frac{0}{120}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4}{2*60}=\frac{8}{120}
=1/15
$