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3/2a-4/3a=-10+22/3a
We move all terms to the left:
3/2a-4/3a-(-10+22/3a)=0
Domain of the equation: 2a!=0
a!=0/2
a!=0
a∈R
Domain of the equation: 3a!=0
a!=0/3
a!=0
a∈R
Domain of the equation: 3a)!=0We add all the numbers together, and all the variables
a!=0/1
a!=0
a∈R
3/2a-4/3a-(22/3a-10)=0
We get rid of parentheses
3/2a-4/3a-22/3a+10=0
We calculate fractions
9a/6a^2+(-44a-4)/6a^2+10=0
We multiply all the terms by the denominator
9a+(-44a-4)+10*6a^2=0
Wy multiply elements
60a^2+9a+(-44a-4)=0
We get rid of parentheses
60a^2+9a-44a-4=0
We add all the numbers together, and all the variables
60a^2-35a-4=0
a = 60; b = -35; c = -4;
Δ = b2-4ac
Δ = -352-4·60·(-4)
Δ = 2185
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}$$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-35)-\sqrt{2185}}{2*60}=\frac{35-\sqrt{2185}}{120} $$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-35)+\sqrt{2185}}{2*60}=\frac{35+\sqrt{2185}}{120} $
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