2b^2+9b=36

Solution for 2b^2+9b=36 equation:

2b^2+9b=36

We move all terms to the left:

2b^2+9b-(36)=0

a = 2; b = 9; c = -36;
Δ = b2-4ac
Δ = 92-4·2·(-36)
Δ = 369
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:

$\sqrt{\Delta}=\sqrt{369}=\sqrt{9*41}=\sqrt{9}*\sqrt{41}=3\sqrt{41}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-3\sqrt{41}}{2*2}=\frac{-9-3\sqrt{41}}{4}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+3\sqrt{41}}{2*2}=\frac{-9+3\sqrt{41}}{4}
$