2/3x-6x=28-3x

Solution for 2/3x-6x=28-3x equation:

2/3x-6x=28-3x

We move all terms to the left:

2/3x-6x-(28-3x)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

2/3x-6x-(-3x+28)=0

We add all the numbers together, and all the variables

-6x+2/3x-(-3x+28)=0

We get rid of parentheses

-6x+2/3x+3x-28=0

We multiply all the terms by the denominator


-6x*3x+3x*3x-28*3x+2=0

Wy multiply elements

-18x^2+9x^2-84x+2=0

We add all the numbers together, and all the variables

-9x^2-84x+2=0

a = -9; b = -84; c = +2;
Δ = b2-4ac
Δ = -842-4·(-9)·2
Δ = 7128
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:

$\sqrt{\Delta}=\sqrt{7128}=\sqrt{324*22}=\sqrt{324}*\sqrt{22}=18\sqrt{22}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-84)-18\sqrt{22}}{2*-9}=\frac{84-18\sqrt{22}}{-18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-84)+18\sqrt{22}}{2*-9}=\frac{84+18\sqrt{22}}{-18}
$