2/9x+1/2x=38

Solution for 2/9x+1/2x=38 equation:

2/9x+1/2x=38

We move all terms to the left:

2/9x+1/2x-(38)=0


Domain of the equation: 9x!=0

x!=0/9

x!=0

x∈R



Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We calculate fractions


4x/18x^2+9x/18x^2-38=0

We multiply all the terms by the denominator


4x+9x-38*18x^2=0

We add all the numbers together, and all the variables

13x-38*18x^2=0

Wy multiply elements

-684x^2+13x=0

a = -684; b = 13; c = 0;
Δ = b2-4ac
Δ = 132-4·(-684)·0
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-13}{2*-684}=\frac{-26}{-1368}
=13/684
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+13}{2*-684}=\frac{0}{-1368}
=0
$