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

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

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

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 9x+1)!=0

x∈R


We get rid of parentheses

1/4x-1/9x-1-4=0

We calculate fractions


9x/36x^2+(-4x)/36x^2-1-4=0

We add all the numbers together, and all the variables

9x/36x^2+(-4x)/36x^2-5=0

We multiply all the terms by the denominator


9x+(-4x)-5*36x^2=0

Wy multiply elements

-180x^2+9x+(-4x)=0

We get rid of parentheses

-180x^2+9x-4x=0

We add all the numbers together, and all the variables

-180x^2+5x=0

a = -180; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·(-180)·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5}{2*-180}=\frac{-10}{-360}
=1/36
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*-180}=\frac{0}{-360}
=0
$