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2/2a+1=5/3a-2
We move all terms to the left:
2/2a+1-(5/3a-2)=0
Domain of the equation: 2a!=0
a!=0/2
a!=0
a∈R
Domain of the equation: 3a-2)!=0We get rid of parentheses
a∈R
2/2a-5/3a+2+1=0
We calculate fractions
6a/6a^2+(-10a)/6a^2+2+1=0
We add all the numbers together, and all the variables
6a/6a^2+(-10a)/6a^2+3=0
We multiply all the terms by the denominator
6a+(-10a)+3*6a^2=0
Wy multiply elements
18a^2+6a+(-10a)=0
We get rid of parentheses
18a^2+6a-10a=0
We add all the numbers together, and all the variables
18a^2-4a=0
a = 18; b = -4; c = 0;
Δ = b2-4ac
Δ = -42-4·18·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{16}=4$$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4}{2*18}=\frac{0}{36} =0 $$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4}{2*18}=\frac{8}{36} =2/9 $
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