6(1/2a-3)-1/2a=0

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Solution for 6(1/2a-3)-1/2a=0 equation:



6(1/2a-3)-1/2a=0
Domain of the equation: 2a-3)!=0
a∈R
Domain of the equation: 2a!=0
a!=0/2
a!=0
a∈R
We multiply parentheses
6a-1/2a-18=0
We multiply all the terms by the denominator
6a*2a-18*2a-1=0
Wy multiply elements
12a^2-36a-1=0
a = 12; b = -36; c = -1;
Δ = b2-4ac
Δ = -362-4·12·(-1)
Δ = 1344
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:
$\sqrt{\Delta}=\sqrt{1344}=\sqrt{64*21}=\sqrt{64}*\sqrt{21}=8\sqrt{21}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-8\sqrt{21}}{2*12}=\frac{36-8\sqrt{21}}{24} $
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+8\sqrt{21}}{2*12}=\frac{36+8\sqrt{21}}{24} $

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