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1/2a+1/3a+3/8=2/3
We move all terms to the left:
1/2a+1/3a+3/8-(2/3)=0
Domain of the equation: 2a!=0
a!=0/2
a!=0
a∈R
Domain of the equation: 3a!=0We add all the numbers together, and all the variables
a!=0/3
a!=0
a∈R
1/2a+1/3a+3/8-(+2/3)=0
We get rid of parentheses
1/2a+1/3a+3/8-2/3=0
We calculate fractions
162a^2/1152a^2+576a/1152a^2+128a/1152a^2+(-256a)/1152a^2=0
We multiply all the terms by the denominator
162a^2+576a+128a+(-256a)=0
We add all the numbers together, and all the variables
162a^2+704a+(-256a)=0
We get rid of parentheses
162a^2+704a-256a=0
We add all the numbers together, and all the variables
162a^2+448a=0
a = 162; b = 448; c = 0;
Δ = b2-4ac
Δ = 4482-4·162·0
Δ = 200704
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{200704}=448$$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(448)-448}{2*162}=\frac{-896}{324} =-2+62/81 $$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(448)+448}{2*162}=\frac{0}{324} =0 $
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