-221=17(b+553)b=

Solution for -221=17(b+553)b= equation:

-221=17(b+553)b=

We move all terms to the left:

-221-(17(b+553)b)=0


We calculate terms in parentheses: -(17(b+553)b), so:

17(b+553)b

We multiply parentheses

17b^2+9401b

Back to the equation:

-(17b^2+9401b)


We get rid of parentheses

-17b^2-9401b-221=0

a = -17; b = -9401; c = -221;
Δ = b2-4ac
Δ = -94012-4·(-17)·(-221)
Δ = 88363773
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:

$\sqrt{\Delta}=\sqrt{88363773}=\sqrt{2601*33973}=\sqrt{2601}*\sqrt{33973}=51\sqrt{33973}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9401)-51\sqrt{33973}}{2*-17}=\frac{9401-51\sqrt{33973}}{-34}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9401)+51\sqrt{33973}}{2*-17}=\frac{9401+51\sqrt{33973}}{-34}
$