2/9x+1/4x=511

Solution for 2/9x+1/4x=511 equation:

2/9x+1/4x=511

We move all terms to the left:

2/9x+1/4x-(511)=0


Domain of the equation: 9x!=0

x!=0/9

x!=0

x∈R



Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We calculate fractions


8x/36x^2+9x/36x^2-511=0

We multiply all the terms by the denominator


8x+9x-511*36x^2=0

We add all the numbers together, and all the variables

17x-511*36x^2=0

Wy multiply elements

-18396x^2+17x=0

a = -18396; b = 17; c = 0;
Δ = b2-4ac
Δ = 172-4·(-18396)·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*-18396}=\frac{-34}{-36792}
=17/18396
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+17}{2*-18396}=\frac{0}{-36792}
=0
$