2/3(x)+4/9(x)=30

Solution for 2/3(x)+4/9(x)=30 equation:

2/3(x)+4/9(x)=30

We move all terms to the left:

2/3(x)+4/9(x)-(30)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 9x!=0

x!=0/9

x!=0

x∈R


We calculate fractions


18x/27x^2+12x/27x^2-30=0

We multiply all the terms by the denominator


18x+12x-30*27x^2=0

We add all the numbers together, and all the variables

30x-30*27x^2=0

Wy multiply elements

-810x^2+30x=0

a = -810; b = 30; c = 0;
Δ = b2-4ac
Δ = 302-4·(-810)·0
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-30}{2*-810}=\frac{-60}{-1620}
=1/27
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+30}{2*-810}=\frac{0}{-1620}
=0
$