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1/a+4=31/2a-5
We move all terms to the left:
1/a+4-(31/2a-5)=0
Domain of the equation: a!=0
a∈R
Domain of the equation: 2a-5)!=0We get rid of parentheses
a∈R
1/a-31/2a+5+4=0
We calculate fractions
2a/2a^2+(-31a)/2a^2+5+4=0
We add all the numbers together, and all the variables
2a/2a^2+(-31a)/2a^2+9=0
We multiply all the terms by the denominator
2a+(-31a)+9*2a^2=0
Wy multiply elements
18a^2+2a+(-31a)=0
We get rid of parentheses
18a^2+2a-31a=0
We add all the numbers together, and all the variables
18a^2-29a=0
a = 18; b = -29; c = 0;
Δ = b2-4ac
Δ = -292-4·18·0
Δ = 841
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{841}=29$$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-29)-29}{2*18}=\frac{0}{36} =0 $$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-29)+29}{2*18}=\frac{58}{36} =1+11/18 $
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