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3/5x+-3=2/3x+-2
We move all terms to the left:
3/5x+-3-(2/3x+-2)=0
Domain of the equation: 5x!=0
x!=0/5
x!=0
x∈R
Domain of the equation: 3x+-2)!=0We add all the numbers together, and all the variables
x∈R
3/5x-(2/3x-2)-3+=0
We add all the numbers together, and all the variables
3/5x-(2/3x-2)=0
We get rid of parentheses
3/5x-2/3x+2=0
We calculate fractions
9x/15x^2+(-10x)/15x^2+2=0
We multiply all the terms by the denominator
9x+(-10x)+2*15x^2=0
Wy multiply elements
30x^2+9x+(-10x)=0
We get rid of parentheses
30x^2+9x-10x=0
We add all the numbers together, and all the variables
30x^2-1x=0
a = 30; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·30·0
Δ = 1
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{1}=1$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-1}{2*30}=\frac{0}{60} =0 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*30}=\frac{2}{60} =1/30 $
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