(2/3)(6x-9)+3x=29

Solution for (2/3)(6x-9)+3x=29 equation:

(2/3)(6x-9)+3x=29

We move all terms to the left:

(2/3)(6x-9)+3x-(29)=0


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

x∈R


We add all the numbers together, and all the variables

(+2/3)(6x-9)+3x-29=0

We add all the numbers together, and all the variables

3x+(+2/3)(6x-9)-29=0

We multiply parentheses ..

(+12x^2+2/3*-9)+3x-29=0

We multiply all the terms by the denominator


(+12x^2+2+3x*3*-9)-29*3*-9)=0

We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

12x^2+3x*3*-7=0

Wy multiply elements

12x^2+9x^2-7=0

We add all the numbers together, and all the variables

21x^2-7=0

a = 21; b = 0; c = -7;
Δ = b2-4ac
Δ = 02-4·21·(-7)
Δ = 588
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:

$\sqrt{\Delta}=\sqrt{588}=\sqrt{196*3}=\sqrt{196}*\sqrt{3}=14\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-14\sqrt{3}}{2*21}=\frac{0-14\sqrt{3}}{42}
=-\frac{14\sqrt{3}}{42}
=-\frac{\sqrt{3}}{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+14\sqrt{3}}{2*21}=\frac{0+14\sqrt{3}}{42}
=\frac{14\sqrt{3}}{42}
=\frac{\sqrt{3}}{3}
$