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-3/2x+9=-2/3x+6
We move all terms to the left:
-3/2x+9-(-2/3x+6)=0
Domain of the equation: 2x!=0
x!=0/2
x!=0
x∈R
Domain of the equation: 3x+6)!=0We get rid of parentheses
x∈R
-3/2x+2/3x-6+9=0
We calculate fractions
(-9x)/6x^2+4x/6x^2-6+9=0
We add all the numbers together, and all the variables
(-9x)/6x^2+4x/6x^2+3=0
We multiply all the terms by the denominator
(-9x)+4x+3*6x^2=0
We add all the numbers together, and all the variables
4x+(-9x)+3*6x^2=0
Wy multiply elements
18x^2+4x+(-9x)=0
We get rid of parentheses
18x^2+4x-9x=0
We add all the numbers together, and all the variables
18x^2-5x=0
a = 18; b = -5; c = 0;
Δ = b2-4ac
Δ = -52-4·18·0
Δ = 25
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{25}=5$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5}{2*18}=\frac{0}{36} =0 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5}{2*18}=\frac{10}{36} =5/18 $
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