1/2a-1/6a=5

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Solution for 1/2a-1/6a=5 equation:



1/2a-1/6a=5
We move all terms to the left:
1/2a-1/6a-(5)=0
Domain of the equation: 2a!=0
a!=0/2
a!=0
a∈R
Domain of the equation: 6a!=0
a!=0/6
a!=0
a∈R
We calculate fractions
6a/12a^2+(-2a)/12a^2-5=0
We multiply all the terms by the denominator
6a+(-2a)-5*12a^2=0
Wy multiply elements
-60a^2+6a+(-2a)=0
We get rid of parentheses
-60a^2+6a-2a=0
We add all the numbers together, and all the variables
-60a^2+4a=0
a = -60; b = 4; c = 0;
Δ = b2-4ac
Δ = 42-4·(-60)·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4}{2*-60}=\frac{-8}{-120} =1/15 $
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4}{2*-60}=\frac{0}{-120} =0 $

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