(1/2x-18)-(24+1/3x)=-15

Solution for (1/2x-18)-(24+1/3x)=-15 equation:

(1/2x-18)-(24+1/3x)=-15

We move all terms to the left:

(1/2x-18)-(24+1/3x)-(-15)=0


Domain of the equation: 2x-18)!=0

x∈R



Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(1/2x-18)-(1/3x+24)-(-15)=0

We add all the numbers together, and all the variables

(1/2x-18)-(1/3x+24)+15=0

We get rid of parentheses

1/2x-1/3x-18-24+15=0

We calculate fractions


3x/6x^2+(-2x)/6x^2-18-24+15=0

We add all the numbers together, and all the variables

3x/6x^2+(-2x)/6x^2-27=0

We multiply all the terms by the denominator


3x+(-2x)-27*6x^2=0

Wy multiply elements

-162x^2+3x+(-2x)=0

We get rid of parentheses

-162x^2+3x-2x=0

We add all the numbers together, and all the variables

-162x^2+x=0

a = -162; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·(-162)·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-1}{2*-162}=\frac{-2}{-324}
=1/162
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*-162}=\frac{0}{-324}
=0
$