6x+1=9x^2

Solution for 6x+1=9x^2 equation:

6x+1=9x^2

We move all terms to the left:

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

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

a = -9; b = 6; c = +1;
Δ = b2-4ac
Δ = 62-4·(-9)·1
Δ = 72
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{72}=\sqrt{36*2}=\sqrt{36}*\sqrt{2}=6\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6\sqrt{2}}{2*-9}=\frac{-6-6\sqrt{2}}{-18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6\sqrt{2}}{2*-9}=\frac{-6+6\sqrt{2}}{-18}
$