4/9x+1/2x=51

Solution for 4/9x+1/2x=51 equation:

4/9x+1/2x=51

We move all terms to the left:

4/9x+1/2x-(51)=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


8x/18x^2+9x/18x^2-51=0

We multiply all the terms by the denominator


8x+9x-51*18x^2=0

We add all the numbers together, and all the variables

17x-51*18x^2=0

Wy multiply elements

-918x^2+17x=0

a = -918; b = 17; c = 0;
Δ = b2-4ac
Δ = 172-4·(-918)·0
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-17}{2*-918}=\frac{-34}{-1836}
=1/54
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+17}{2*-918}=\frac{0}{-1836}
=0
$