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16/5a-5/16a=462

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Solution for 16/5a-5/16a=462 equation:



16/5a-5/16a=462
We move all terms to the left:
16/5a-5/16a-(462)=0
Domain of the equation: 5a!=0
a!=0/5
a!=0
a∈R
Domain of the equation: 16a!=0
a!=0/16
a!=0
a∈R
We calculate fractions
256a/80a^2+(-25a)/80a^2-462=0
We multiply all the terms by the denominator
256a+(-25a)-462*80a^2=0
Wy multiply elements
-36960a^2+256a+(-25a)=0
We get rid of parentheses
-36960a^2+256a-25a=0
We add all the numbers together, and all the variables
-36960a^2+231a=0
a = -36960; b = 231; c = 0;
Δ = b2-4ac
Δ = 2312-4·(-36960)·0
Δ = 53361
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{53361}=231
a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(231)-231}{2*-36960}=\frac{-462}{-73920} =1/160
a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(231)+231}{2*-36960}=\frac{0}{-73920} =0

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