4/9x+11/18x=29

Solution for 4/9x+11/18x=29 equation:

4/9x+11/18x=29

We move all terms to the left:

4/9x+11/18x-(29)=0


Domain of the equation: 9x!=0

x!=0/9

x!=0

x∈R



Domain of the equation: 18x!=0

x!=0/18

x!=0

x∈R


We calculate fractions


72x/162x^2+99x/162x^2-29=0

We multiply all the terms by the denominator


72x+99x-29*162x^2=0

We add all the numbers together, and all the variables

171x-29*162x^2=0

Wy multiply elements

-4698x^2+171x=0

a = -4698; b = 171; c = 0;
Δ = b2-4ac
Δ = 1712-4·(-4698)·0
Δ = 29241
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{29241}=171$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(171)-171}{2*-4698}=\frac{-342}{-9396}
=19/522
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(171)+171}{2*-4698}=\frac{0}{-9396}
=0
$