9x=2/3x-1

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

9x=2/3x-1

We move all terms to the left:

9x-(2/3x-1)=0


Domain of the equation: 3x-1)!=0

x∈R


We get rid of parentheses

9x-2/3x+1=0

We multiply all the terms by the denominator


9x*3x+1*3x-2=0

Wy multiply elements

27x^2+3x-2=0

a = 27; b = 3; c = -2;
Δ = b2-4ac
Δ = 32-4·27·(-2)
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-15}{2*27}=\frac{-18}{54}
=-1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+15}{2*27}=\frac{12}{54}
=2/9
$