x=2/3x-9

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

x=2/3x-9

We move all terms to the left:

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


Domain of the equation: 3x-9)!=0

x∈R


We get rid of parentheses

x-2/3x+9=0

We multiply all the terms by the denominator


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

Wy multiply elements

3x^2+27x-2=0

a = 3; b = 27; c = -2;
Δ = b2-4ac
Δ = 272-4·3·(-2)
Δ = 753
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-\sqrt{753}}{2*3}=\frac{-27-\sqrt{753}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+\sqrt{753}}{2*3}=\frac{-27+\sqrt{753}}{6}
$