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5/2x+7=2/3x-2
We move all terms to the left:
5/2x+7-(2/3x-2)=0
Domain of the equation: 2x!=0
x!=0/2
x!=0
x∈R
Domain of the equation: 3x-2)!=0We get rid of parentheses
x∈R
5/2x-2/3x+2+7=0
We calculate fractions
15x/6x^2+(-4x)/6x^2+2+7=0
We add all the numbers together, and all the variables
15x/6x^2+(-4x)/6x^2+9=0
We multiply all the terms by the denominator
15x+(-4x)+9*6x^2=0
Wy multiply elements
54x^2+15x+(-4x)=0
We get rid of parentheses
54x^2+15x-4x=0
We add all the numbers together, and all the variables
54x^2+11x=0
a = 54; b = 11; c = 0;
Δ = b2-4ac
Δ = 112-4·54·0
Δ = 121
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{121}=11$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-11}{2*54}=\frac{-22}{108} =-11/54 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+11}{2*54}=\frac{0}{108} =0 $
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