-2/3x+6=9x

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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} $

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