1/2a-6=3+a

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Solution for 1/2a-6=3+a equation:



1/2a-6=3+a
We move all terms to the left:
1/2a-6-(3+a)=0
Domain of the equation: 2a!=0
a!=0/2
a!=0
a∈R
We add all the numbers together, and all the variables
1/2a-(a+3)-6=0
We get rid of parentheses
1/2a-a-3-6=0
We multiply all the terms by the denominator
-a*2a-3*2a-6*2a+1=0
Wy multiply elements
-2a^2-6a-12a+1=0
We add all the numbers together, and all the variables
-2a^2-18a+1=0
a = -2; b = -18; c = +1;
Δ = b2-4ac
Δ = -182-4·(-2)·1
Δ = 332
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:
$\sqrt{\Delta}=\sqrt{332}=\sqrt{4*83}=\sqrt{4}*\sqrt{83}=2\sqrt{83}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{83}}{2*-2}=\frac{18-2\sqrt{83}}{-4} $
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{83}}{2*-2}=\frac{18+2\sqrt{83}}{-4} $

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