9=2b(b+5)

Solution for 9=2b(b+5) equation:

9=2b(b+5)

We move all terms to the left:

9-(2b(b+5))=0


We calculate terms in parentheses: -(2b(b+5)), so:

2b(b+5)

We multiply parentheses

2b^2+10b

Back to the equation:

-(2b^2+10b)


We get rid of parentheses

-2b^2-10b+9=0

a = -2; b = -10; c = +9;
Δ = b2-4ac
Δ = -102-4·(-2)·9
Δ = 172
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:

$\sqrt{\Delta}=\sqrt{172}=\sqrt{4*43}=\sqrt{4}*\sqrt{43}=2\sqrt{43}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{43}}{2*-2}=\frac{10-2\sqrt{43}}{-4}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{43}}{2*-2}=\frac{10+2\sqrt{43}}{-4}
$