54/x+63/(x+6)=3

Solution for 54/x+63/(x+6)=3 equation:

54/x+63/(x+6)=3

We move all terms to the left:

54/x+63/(x+6)-(3)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: (x+6)!=0

We move all terms containing x to the left, all other terms to the right

x!=-6

x∈R


We calculate fractions


(54x+324)/(x^2+6x)+63x/(x^2+6x)-3=0

We multiply all the terms by the denominator


(54x+324)+63x-3*(x^2+6x)=0

We add all the numbers together, and all the variables

63x+(54x+324)-3*(x^2+6x)=0

We multiply parentheses

-3x^2+63x+(54x+324)-18x=0

We get rid of parentheses

-3x^2+63x+54x-18x+324=0

We add all the numbers together, and all the variables

-3x^2+99x+324=0

a = -3; b = 99; c = +324;
Δ = b2-4ac
Δ = 992-4·(-3)·324
Δ = 13689
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{13689}=117$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(99)-117}{2*-3}=\frac{-216}{-6}
=+36
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(99)+117}{2*-3}=\frac{18}{-6}
=-3
$