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

Wy multiply elements

-918x^2+8x+(-9x)=0

We get rid of parentheses

-918x^2+8x-9x=0

We add all the numbers together, and all the variables

-918x^2-1x=0

a = -918; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·(-918)·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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