-2/3x+6=9x

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

-2/3x+6=9x

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


-9x*3x+6*3x-2=0

Wy multiply elements

-27x^2+18x-2=0

a = -27; b = 18; c = -2;
Δ = b2-4ac
Δ = 182-4·(-27)·(-2)
Δ = 108
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{108}=\sqrt{36*3}=\sqrt{36}*\sqrt{3}=6\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-6\sqrt{3}}{2*-27}=\frac{-18-6\sqrt{3}}{-54}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+6\sqrt{3}}{2*-27}=\frac{-18+6\sqrt{3}}{-54}
$