1/2a-6+a=21

Solution for 1/2a-6+a=21 equation:

1/2a-6+a=21

We move all terms to the left:

1/2a-6+a-(21)=0


Domain of the equation: 2a!=0

a!=0/2

a!=0

a∈R


We add all the numbers together, and all the variables

a+1/2a-27=0

We multiply all the terms by the denominator


a*2a-27*2a+1=0

Wy multiply elements

2a^2-54a+1=0

a = 2; b = -54; c = +1;
Δ = b2-4ac
Δ = -542-4·2·1
Δ = 2908
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:

$\sqrt{\Delta}=\sqrt{2908}=\sqrt{4*727}=\sqrt{4}*\sqrt{727}=2\sqrt{727}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-54)-2\sqrt{727}}{2*2}=\frac{54-2\sqrt{727}}{4}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-54)+2\sqrt{727}}{2*2}=\frac{54+2\sqrt{727}}{4}
$