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

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

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

We move all terms to the left:

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

-9a^2+3a-21a+1=0

We add all the numbers together, and all the variables

-9a^2-18a+1=0

a = -9; b = -18; c = +1;
Δ = b2-4ac
Δ = -182-4·(-9)·1
Δ = 360
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:

$\sqrt{\Delta}=\sqrt{360}=\sqrt{36*10}=\sqrt{36}*\sqrt{10}=6\sqrt{10}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-6\sqrt{10}}{2*-9}=\frac{18-6\sqrt{10}}{-18}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+6\sqrt{10}}{2*-9}=\frac{18+6\sqrt{10}}{-18}
$