4a/2a=54-a

Solution for 4a/2a=54-a equation:

4a/2a=54-a

We move all terms to the left:

4a/2a-(54-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

4a/2a-(-1a+54)=0

We get rid of parentheses

4a/2a+1a-54=0

We multiply all the terms by the denominator


4a+1a*2a-54*2a=0

Wy multiply elements

2a^2+4a-108a=0

We add all the numbers together, and all the variables

2a^2-104a=0

a = 2; b = -104; c = 0;
Δ = b2-4ac
Δ = -1042-4·2·0
Δ = 10816
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{10816}=104$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-104)-104}{2*2}=\frac{0}{4}
=0
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-104)+104}{2*2}=\frac{208}{4}
=52
$