9x2=2x+1

Solution for 9x2=2x+1 equation:

9x^2=2x+1

We move all terms to the left:

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

We get rid of parentheses

9x^2-2x-1=0

a = 9; b = -2; c = -1;
Δ = b2-4ac
Δ = -22-4·9·(-1)
Δ = 40
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:

$\sqrt{\Delta}=\sqrt{40}=\sqrt{4*10}=\sqrt{4}*\sqrt{10}=2\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{10}}{2*9}=\frac{2-2\sqrt{10}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{10}}{2*9}=\frac{2+2\sqrt{10}}{18}
$