(2/3)(3x+18)=5x-9

Solution for (2/3)(3x+18)=5x-9 equation:

(2/3)(3x+18)=5x-9

We move all terms to the left:

(2/3)(3x+18)-(5x-9)=0


Domain of the equation: 3)(3x+18)!=0

x∈R


We add all the numbers together, and all the variables

(+2/3)(3x+18)-(5x-9)=0

We get rid of parentheses

(+2/3)(3x+18)-5x+9=0

We multiply parentheses ..

(+6x^2+2/3*18)-5x+9=0

We multiply all the terms by the denominator


(+6x^2+2-5x*3*18)+9*3*18)=0

We add all the numbers together, and all the variables

(+6x^2+2-5x*3*18)=0

We get rid of parentheses

6x^2-5x*3*18+2=0

Wy multiply elements

6x^2-270x*1+2=0

Wy multiply elements

6x^2-270x+2=0

a = 6; b = -270; c = +2;
Δ = b2-4ac
Δ = -2702-4·6·2
Δ = 72852
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:

$\sqrt{\Delta}=\sqrt{72852}=\sqrt{4*18213}=\sqrt{4}*\sqrt{18213}=2\sqrt{18213}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-270)-2\sqrt{18213}}{2*6}=\frac{270-2\sqrt{18213}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-270)+2\sqrt{18213}}{2*6}=\frac{270+2\sqrt{18213}}{12}
$