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3/2x+6=-2/3x+12
We move all terms to the left:
3/2x+6-(-2/3x+12)=0
Domain of the equation: 2x!=0
x!=0/2
x!=0
x∈R
Domain of the equation: 3x+12)!=0We get rid of parentheses
x∈R
3/2x+2/3x-12+6=0
We calculate fractions
9x/6x^2+4x/6x^2-12+6=0
We add all the numbers together, and all the variables
9x/6x^2+4x/6x^2-6=0
We multiply all the terms by the denominator
9x+4x-6*6x^2=0
We add all the numbers together, and all the variables
13x-6*6x^2=0
Wy multiply elements
-36x^2+13x=0
a = -36; b = 13; c = 0;
Δ = b2-4ac
Δ = 132-4·(-36)·0
Δ = 169
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{169}=13$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-13}{2*-36}=\frac{-26}{-72} =13/36 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+13}{2*-36}=\frac{0}{-72} =0 $
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