5/3x+1/3x=21/3+7x

Solution for 5/3x+1/3x=21/3+7x equation:

5/3x+1/3x=21/3+7x

We move all terms to the left:

5/3x+1/3x-(21/3+7x)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 3+7x)!=0

We move all terms containing x to the left, all other terms to the right

7x)!=-3

x!=-3/1

x!=-3

x∈R


We add all the numbers together, and all the variables

5/3x+1/3x-(7x+7)=0

We get rid of parentheses

5/3x+1/3x-7x-7=0

We multiply all the terms by the denominator


-7x*3x-7*3x+5+1=0

We add all the numbers together, and all the variables

-7x*3x-7*3x+6=0

Wy multiply elements

-21x^2-21x+6=0

a = -21; b = -21; c = +6;
Δ = b2-4ac
Δ = -212-4·(-21)·6
Δ = 945
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:

$\sqrt{\Delta}=\sqrt{945}=\sqrt{9*105}=\sqrt{9}*\sqrt{105}=3\sqrt{105}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-3\sqrt{105}}{2*-21}=\frac{21-3\sqrt{105}}{-42}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+3\sqrt{105}}{2*-21}=\frac{21+3\sqrt{105}}{-42}
$