18/(x-3)=24-3x

Solution for 18/(x-3)=24-3x equation:

18/(x-3)=24-3x

We move all terms to the left:

18/(x-3)-(24-3x)=0


Domain of the equation: (x-3)!=0

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

x!=3

x∈R


We add all the numbers together, and all the variables

18/(x-3)-(-3x+24)=0

We get rid of parentheses

18/(x-3)+3x-24=0

We multiply all the terms by the denominator


3x*(x-3)-24*(x-3)+18=0

We multiply parentheses

3x^2-9x-24x+72+18=0

We add all the numbers together, and all the variables

3x^2-33x+90=0

a = 3; b = -33; c = +90;
Δ = b2-4ac
Δ = -332-4·3·90
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-33)-3}{2*3}=\frac{30}{6}
=5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-33)+3}{2*3}=\frac{36}{6}
=6
$