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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)!=0We add all the numbers together, and all the variables
x!=0/1
x!=0
x∈R
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 $
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