4-1/2a=6-a

Solution for 4-1/2a=6-a equation:

4-1/2a=6-a

We move all terms to the left:

4-1/2a-(6-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-(-1a+6)+4=0

We get rid of parentheses

-1/2a+1a-6+4=0

We multiply all the terms by the denominator


1a*2a-6*2a+4*2a-1=0

Wy multiply elements

2a^2-12a+8a-1=0

We add all the numbers together, and all the variables

2a^2-4a-1=0

a = 2; b = -4; c = -1;
Δ = b2-4ac
Δ = -42-4·2·(-1)
Δ = 24
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:

$\sqrt{\Delta}=\sqrt{24}=\sqrt{4*6}=\sqrt{4}*\sqrt{6}=2\sqrt{6}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{6}}{2*2}=\frac{4-2\sqrt{6}}{4}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{6}}{2*2}=\frac{4+2\sqrt{6}}{4}
$