(2/3)(6x+18)=-9x+2-2x

Solution for (2/3)(6x+18)=-9x+2-2x equation:

(2/3)(6x+18)=-9x+2-2x

We move all terms to the left:

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


Domain of the equation: 3)(6x+18)!=0

x∈R


We add all the numbers together, and all the variables

(+2/3)(6x+18)-(-11x+2)=0

We get rid of parentheses

(+2/3)(6x+18)+11x-2=0

We multiply parentheses ..

(+12x^2+2/3*18)+11x-2=0

We multiply all the terms by the denominator


(+12x^2+2+11x*3*18)-2*3*18)=0

We add all the numbers together, and all the variables

(+12x^2+2+11x*3*18)=0

We get rid of parentheses

12x^2+11x*3*18+2=0

Wy multiply elements

12x^2+594x*1+2=0

Wy multiply elements

12x^2+594x+2=0

a = 12; b = 594; c = +2;
Δ = b2-4ac
Δ = 5942-4·12·2
Δ = 352740
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:

$\sqrt{\Delta}=\sqrt{352740}=\sqrt{4*88185}=\sqrt{4}*\sqrt{88185}=2\sqrt{88185}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(594)-2\sqrt{88185}}{2*12}=\frac{-594-2\sqrt{88185}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(594)+2\sqrt{88185}}{2*12}=\frac{-594+2\sqrt{88185}}{24}
$