2b=3-9b^2

Solution for 2b=3-9b^2 equation:

2b=3-9b^2

We move all terms to the left:

2b-(3-9b^2)=0

We get rid of parentheses

9b^2+2b-3=0

a = 9; b = 2; c = -3;
Δ = b2-4ac
Δ = 22-4·9·(-3)
Δ = 112
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{112}=\sqrt{16*7}=\sqrt{16}*\sqrt{7}=4\sqrt{7}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-4\sqrt{7}}{2*9}=\frac{-2-4\sqrt{7}}{18}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+4\sqrt{7}}{2*9}=\frac{-2+4\sqrt{7}}{18}
$