x=(x+5x-9)*(2/3)

Solution for x=(x+5x-9)*(2/3) equation:

x=(x+5x-9)(2/3)

We move all terms to the left:

x-((x+5x-9)(2/3))=0

We add all the numbers together, and all the variables

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

We multiply parentheses ..

-((+12x^2-9*2/3))+x=0

We multiply all the terms by the denominator


-((+12x^2-9*2+x*3))=0


We calculate terms in parentheses: -((+12x^2-9*2+x*3)), so:

(+12x^2-9*2+x*3)

We get rid of parentheses

12x^2+x*3-9*2

We add all the numbers together, and all the variables

12x^2+x*3-18

Wy multiply elements

12x^2+3x-18

Back to the equation:

-(12x^2+3x-18)


We get rid of parentheses

-12x^2-3x+18=0

a = -12; b = -3; c = +18;
Δ = b2-4ac
Δ = -32-4·(-12)·18
Δ = 873
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:

$\sqrt{\Delta}=\sqrt{873}=\sqrt{9*97}=\sqrt{9}*\sqrt{97}=3\sqrt{97}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3\sqrt{97}}{2*-12}=\frac{3-3\sqrt{97}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3\sqrt{97}}{2*-12}=\frac{3+3\sqrt{97}}{-24}
$