5/2x-12=18-1/3x

Solution for 5/2x-12=18-1/3x equation:

5/2x-12=18-1/3x

We move all terms to the left:

5/2x-12-(18-1/3x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=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

5/2x-(-1/3x+18)-12=0

We get rid of parentheses

5/2x+1/3x-18-12=0

We calculate fractions


15x/6x^2+2x/6x^2-18-12=0

We add all the numbers together, and all the variables

15x/6x^2+2x/6x^2-30=0

We multiply all the terms by the denominator


15x+2x-30*6x^2=0

We add all the numbers together, and all the variables

17x-30*6x^2=0

Wy multiply elements

-180x^2+17x=0

a = -180; b = 17; c = 0;
Δ = b2-4ac
Δ = 172-4·(-180)·0
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-17}{2*-180}=\frac{-34}{-360}
=17/180
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+17}{2*-180}=\frac{0}{-360}
=0
$