1/2a=4-a

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

1/2a=4-a

We move all terms to the left:

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

We get rid of parentheses

1/2a+1a-4=0

We multiply all the terms by the denominator


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

Wy multiply elements

2a^2-8a+1=0

a = 2; b = -8; c = +1;
Δ = b2-4ac
Δ = -82-4·2·1
Δ = 56
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:

$\sqrt{\Delta}=\sqrt{56}=\sqrt{4*14}=\sqrt{4}*\sqrt{14}=2\sqrt{14}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{14}}{2*2}=\frac{8-2\sqrt{14}}{4}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{14}}{2*2}=\frac{8+2\sqrt{14}}{4}
$