3/1+a=2/2a+6

Solution for 3/1+a=2/2a+6 equation:

3/1+a=2/2a+6

We move all terms to the left:

3/1+a-(2/2a+6)=0


Domain of the equation: 2a+6)!=0

a∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

a-2/2a-6=0

We multiply all the terms by the denominator


a*2a-6*2a-2=0

Wy multiply elements

2a^2-12a-2=0

a = 2; b = -12; c = -2;
Δ = b2-4ac
Δ = -122-4·2·(-2)
Δ = 160
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:

$\sqrt{\Delta}=\sqrt{160}=\sqrt{16*10}=\sqrt{16}*\sqrt{10}=4\sqrt{10}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{10}}{2*2}=\frac{12-4\sqrt{10}}{4}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{10}}{2*2}=\frac{12+4\sqrt{10}}{4}
$