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1/2a-5+7/a=2/a+5
We move all terms to the left:
1/2a-5+7/a-(2/a+5)=0
Domain of the equation: 2a!=0
a!=0/2
a!=0
a∈R
Domain of the equation: a!=0
a∈R
Domain of the equation: a+5)!=0We get rid of parentheses
a∈R
1/2a+7/a-2/a-5-5=0
We calculate fractions
a/2a^2+(-4a+7)/2a^2-5-5=0
We add all the numbers together, and all the variables
a/2a^2+(-4a+7)/2a^2-10=0
We multiply all the terms by the denominator
a+(-4a+7)-10*2a^2=0
Wy multiply elements
-20a^2+a+(-4a+7)=0
We get rid of parentheses
-20a^2+a-4a+7=0
We add all the numbers together, and all the variables
-20a^2-3a+7=0
a = -20; b = -3; c = +7;
Δ = b2-4ac
Δ = -32-4·(-20)·7
Δ = 569
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{-(-3)-\sqrt{569}}{2*-20}=\frac{3-\sqrt{569}}{-40} $$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{569}}{2*-20}=\frac{3+\sqrt{569}}{-40} $
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