2b^2+17b=-21

Solution for 2b^2+17b=-21 equation:

2b^2+17b=-21

We move all terms to the left:

2b^2+17b-(-21)=0

We add all the numbers together, and all the variables

2b^2+17b+21=0

a = 2; b = 17; c = +21;
Δ = b2-4ac
Δ = 172-4·2·21
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-11}{2*2}=\frac{-28}{4}
=-7
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+11}{2*2}=\frac{-6}{4}
=-1+1/2
$