3b^2+9b-21=0

Solution for 3b^2+9b-21=0 equation:

3b^2+9b-21=0

a = 3; b = 9; c = -21;
Δ = b2-4ac
Δ = 92-4·3·(-21)
Δ = 333
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:

$\sqrt{\Delta}=\sqrt{333}=\sqrt{9*37}=\sqrt{9}*\sqrt{37}=3\sqrt{37}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-3\sqrt{37}}{2*3}=\frac{-9-3\sqrt{37}}{6}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+3\sqrt{37}}{2*3}=\frac{-9+3\sqrt{37}}{6}
$