2/3x-7(x+4)=1/3x

Solution for 2/3x-7(x+4)=1/3x equation:

2/3x-7(x+4)=1/3x

We move all terms to the left:

2/3x-7(x+4)-(1/3x)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

2/3x-7(x+4)-(+1/3x)=0

We multiply parentheses

2/3x-7x-(+1/3x)-28=0

We get rid of parentheses

2/3x-7x-1/3x-28=0

We multiply all the terms by the denominator


-7x*3x-28*3x+2-1=0

We add all the numbers together, and all the variables

-7x*3x-28*3x+1=0

Wy multiply elements

-21x^2-84x+1=0

a = -21; b = -84; c = +1;
Δ = b2-4ac
Δ = -842-4·(-21)·1
Δ = 7140
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:

$\sqrt{\Delta}=\sqrt{7140}=\sqrt{4*1785}=\sqrt{4}*\sqrt{1785}=2\sqrt{1785}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-84)-2\sqrt{1785}}{2*-21}=\frac{84-2\sqrt{1785}}{-42}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-84)+2\sqrt{1785}}{2*-21}=\frac{84+2\sqrt{1785}}{-42}
$