-4/9x-5/36+1/4x=-36

Solution for -4/9x-5/36+1/4x=-36 equation:

-4/9x-5/36+1/4x=-36

We move all terms to the left:

-4/9x-5/36+1/4x-(-36)=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 add all the numbers together, and all the variables

-4/9x+1/4x+36-5/36=0

We calculate fractions


(-720x^2)/3888x^2+(-1728x)/3888x^2+972x/3888x^2+36=0

We multiply all the terms by the denominator


(-720x^2)+(-1728x)+972x+36*3888x^2=0

We add all the numbers together, and all the variables

(-720x^2)+972x+(-1728x)+36*3888x^2=0

Wy multiply elements

(-720x^2)+139968x^2+972x+(-1728x)=0

We get rid of parentheses

-720x^2+139968x^2+972x-1728x=0

We add all the numbers together, and all the variables

139248x^2-756x=0

a = 139248; b = -756; c = 0;
Δ = b2-4ac
Δ = -7562-4·139248·0
Δ = 571536
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{571536}=756$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-756)-756}{2*139248}=\frac{0}{278496}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-756)+756}{2*139248}=\frac{1512}{278496}
=21/3868
$