1/48a-4=a+8-2a

Solution for 1/48a-4=a+8-2a equation:

1/48a-4=a+8-2a

We move all terms to the left:

1/48a-4-(a+8-2a)=0


Domain of the equation: 48a!=0

a!=0/48

a!=0

a∈R


We add all the numbers together, and all the variables

1/48a-(-1a+8)-4=0

We get rid of parentheses

1/48a+1a-8-4=0

We multiply all the terms by the denominator


1a*48a-8*48a-4*48a+1=0

Wy multiply elements

48a^2-384a-192a+1=0

We add all the numbers together, and all the variables

48a^2-576a+1=0

a = 48; b = -576; c = +1;
Δ = b2-4ac
Δ = -5762-4·48·1
Δ = 331584
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:

$\sqrt{\Delta}=\sqrt{331584}=\sqrt{64*5181}=\sqrt{64}*\sqrt{5181}=8\sqrt{5181}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-576)-8\sqrt{5181}}{2*48}=\frac{576-8\sqrt{5181}}{96}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-576)+8\sqrt{5181}}{2*48}=\frac{576+8\sqrt{5181}}{96}
$