2/3x+7/3x=3x

Solution for 2/3x+7/3x=3x equation:

2/3x+7/3x=3x

We move all terms to the left:

2/3x+7/3x-(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

-3x+2/3x+7/3x=0

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

-3x*3x+9=0

Wy multiply elements

-9x^2+9=0

a = -9; b = 0; c = +9;
Δ = b2-4ac
Δ = 02-4·(-9)·9
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-18}{2*-9}=\frac{-18}{-18}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+18}{2*-9}=\frac{18}{-18}
=-1
$