3-(2/3)(6x-9)=5-2x

Solution for 3-(2/3)(6x-9)=5-2x equation:

3-(2/3)(6x-9)=5-2x

We move all terms to the left:

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

We get rid of parentheses

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

We multiply parentheses ..

-(+12x^2+2/3*-9)+2x-5+3=0

We multiply all the terms by the denominator


-(+12x^2+2+2x*3*-9)-5*3*-9)+3*3*-9)=0

We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

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

Wy multiply elements

-12x^2-6x^2+7=0

We add all the numbers together, and all the variables

-18x^2+7=0

a = -18; b = 0; c = +7;
Δ = b2-4ac
Δ = 02-4·(-18)·7
Δ = 504
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:

$\sqrt{\Delta}=\sqrt{504}=\sqrt{36*14}=\sqrt{36}*\sqrt{14}=6\sqrt{14}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{14}}{2*-18}=\frac{0-6\sqrt{14}}{-36}
=-\frac{6\sqrt{14}}{-36}
=-\frac{\sqrt{14}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{14}}{2*-18}=\frac{0+6\sqrt{14}}{-36}
=\frac{6\sqrt{14}}{-36}
=\frac{\sqrt{14}}{-6}
$