3+a=7/3a+1

Solution for 3+a=7/3a+1 equation:

3+a=7/3a+1

We move all terms to the left:

3+a-(7/3a+1)=0


Domain of the equation: 3a+1)!=0

a∈R


We get rid of parentheses

a-7/3a-1+3=0

We multiply all the terms by the denominator


a*3a-1*3a+3*3a-7=0

Wy multiply elements

3a^2-3a+9a-7=0

We add all the numbers together, and all the variables

3a^2+6a-7=0

a = 3; b = 6; c = -7;
Δ = b2-4ac
Δ = 62-4·3·(-7)
Δ = 120
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:

$\sqrt{\Delta}=\sqrt{120}=\sqrt{4*30}=\sqrt{4}*\sqrt{30}=2\sqrt{30}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{30}}{2*3}=\frac{-6-2\sqrt{30}}{6}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{30}}{2*3}=\frac{-6+2\sqrt{30}}{6}
$