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2/3x+7=3/2x
We move all terms to the left:
2/3x+7-(3/2x)=0
Domain of the equation: 3x!=0
x!=0/3
x!=0
x∈R
Domain of the equation: 2x)!=0We add all the numbers together, and all the variables
x!=0/1
x!=0
x∈R
2/3x-(+3/2x)+7=0
We get rid of parentheses
2/3x-3/2x+7=0
We calculate fractions
4x/6x^2+(-9x)/6x^2+7=0
We multiply all the terms by the denominator
4x+(-9x)+7*6x^2=0
Wy multiply elements
42x^2+4x+(-9x)=0
We get rid of parentheses
42x^2+4x-9x=0
We add all the numbers together, and all the variables
42x^2-5x=0
a = 42; b = -5; c = 0;
Δ = b2-4ac
Δ = -52-4·42·0
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$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5}{2*42}=\frac{0}{84} =0 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5}{2*42}=\frac{10}{84} =5/42 $
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