2b^2=-9b-1

Solution for 2b^2=-9b-1 equation:

2b^2=-9b-1

We move all terms to the left:

2b^2-(-9b-1)=0

We get rid of parentheses

2b^2+9b+1=0

a = 2; b = 9; c = +1;
Δ = b2-4ac
Δ = 92-4·2·1
Δ = 73
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-\sqrt{73}}{2*2}=\frac{-9-\sqrt{73}}{4}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{73}}{2*2}=\frac{-9+\sqrt{73}}{4}
$