4/3x-1/3x=x+7

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

4/3x-1/3x=x+7

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

4/3x-1/3x-x-7=0

We multiply all the terms by the denominator


-x*3x-7*3x+4-1=0

We add all the numbers together, and all the variables

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

Wy multiply elements

-3x^2-21x+3=0

a = -3; b = -21; c = +3;
Δ = b2-4ac
Δ = -212-4·(-3)·3
Δ = 477
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:

$\sqrt{\Delta}=\sqrt{477}=\sqrt{9*53}=\sqrt{9}*\sqrt{53}=3\sqrt{53}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-3\sqrt{53}}{2*-3}=\frac{21-3\sqrt{53}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+3\sqrt{53}}{2*-3}=\frac{21+3\sqrt{53}}{-6}
$