6/9x+2/3x=7

Solution for 6/9x+2/3x=7 equation:

6/9x+2/3x=7

We move all terms to the left:

6/9x+2/3x-(7)=0


Domain of the equation: 9x!=0

x!=0/9

x!=0

x∈R



Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We calculate fractions


18x/27x^2+18x/27x^2-7=0

We multiply all the terms by the denominator


18x+18x-7*27x^2=0

We add all the numbers together, and all the variables

36x-7*27x^2=0

Wy multiply elements

-189x^2+36x=0

a = -189; b = 36; c = 0;
Δ = b2-4ac
Δ = 362-4·(-189)·0
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-36}{2*-189}=\frac{-72}{-378}
=4/21
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+36}{2*-189}=\frac{0}{-378}
=0
$