2b(b+9)=17

Solution for 2b(b+9)=17 equation:

2b(b+9)=17

We move all terms to the left:

2b(b+9)-(17)=0

We multiply parentheses

2b^2+18b-17=0

a = 2; b = 18; c = -17;
Δ = b2-4ac
Δ = 182-4·2·(-17)
Δ = 460
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:

$\sqrt{\Delta}=\sqrt{460}=\sqrt{4*115}=\sqrt{4}*\sqrt{115}=2\sqrt{115}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-2\sqrt{115}}{2*2}=\frac{-18-2\sqrt{115}}{4}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+2\sqrt{115}}{2*2}=\frac{-18+2\sqrt{115}}{4}
$