1/3a=7-3a

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

1/3a=7-3a

We move all terms to the left:

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


Domain of the equation: 3a!=0

a!=0/3

a!=0

a∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

1/3a+3a-7=0

We multiply all the terms by the denominator


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

Wy multiply elements

9a^2-21a+1=0

a = 9; b = -21; c = +1;
Δ = b2-4ac
Δ = -212-4·9·1
Δ = 405
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:

$\sqrt{\Delta}=\sqrt{405}=\sqrt{81*5}=\sqrt{81}*\sqrt{5}=9\sqrt{5}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-9\sqrt{5}}{2*9}=\frac{21-9\sqrt{5}}{18}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+9\sqrt{5}}{2*9}=\frac{21+9\sqrt{5}}{18}
$