(2/3)(9x+6)=6x+4

Solution for (2/3)(9x+6)=6x+4 equation:

(2/3)(9x+6)=6x+4

We move all terms to the left:

(2/3)(9x+6)-(6x+4)=0


Domain of the equation: 3)(9x+6)!=0

x∈R


We add all the numbers together, and all the variables

(+2/3)(9x+6)-(6x+4)=0

We get rid of parentheses

(+2/3)(9x+6)-6x-4=0

We multiply parentheses ..

(+18x^2+2/3*6)-6x-4=0

We multiply all the terms by the denominator


(+18x^2+2-6x*3*6)-4*3*6)=0

We add all the numbers together, and all the variables

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

We get rid of parentheses

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

Wy multiply elements

18x^2-108x*6+2=0

Wy multiply elements

18x^2-648x+2=0

a = 18; b = -648; c = +2;
Δ = b2-4ac
Δ = -6482-4·18·2
Δ = 419760
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:

$\sqrt{\Delta}=\sqrt{419760}=\sqrt{144*2915}=\sqrt{144}*\sqrt{2915}=12\sqrt{2915}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-648)-12\sqrt{2915}}{2*18}=\frac{648-12\sqrt{2915}}{36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-648)+12\sqrt{2915}}{2*18}=\frac{648+12\sqrt{2915}}{36}
$