9a(a-2)+3a=1

Solution for 9a(a-2)+3a=1 equation:

9a(a-2)+3a=1

We move all terms to the left:

9a(a-2)+3a-(1)=0

We add all the numbers together, and all the variables

3a+9a(a-2)-1=0

We multiply parentheses

9a^2+3a-18a-1=0

We add all the numbers together, and all the variables

9a^2-15a-1=0

a = 9; b = -15; c = -1;
Δ = b2-4ac
Δ = -152-4·9·(-1)
Δ = 261
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:

$\sqrt{\Delta}=\sqrt{261}=\sqrt{9*29}=\sqrt{9}*\sqrt{29}=3\sqrt{29}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-3\sqrt{29}}{2*9}=\frac{15-3\sqrt{29}}{18}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+3\sqrt{29}}{2*9}=\frac{15+3\sqrt{29}}{18}
$