3x+1=9x2+6x+1

Solution for 3x+1=9x2+6x+1 equation:

3x+1=9x^2+6x+1

We move all terms to the left:

3x+1-(9x^2+6x+1)=0

We get rid of parentheses

-9x^2+3x-6x-1+1=0

We add all the numbers together, and all the variables

-9x^2-3x=0

a = -9; b = -3; c = 0;
Δ = b2-4ac
Δ = -32-4·(-9)·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3}{2*-9}=\frac{0}{-18}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3}{2*-9}=\frac{6}{-18}
=-1/3
$