5b(b+6)=18

Solution for 5b(b+6)=18 equation:

5b(b+6)=18

We move all terms to the left:

5b(b+6)-(18)=0

We multiply parentheses

5b^2+30b-18=0

a = 5; b = 30; c = -18;
Δ = b2-4ac
Δ = 302-4·5·(-18)
Δ = 1260
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:

$\sqrt{\Delta}=\sqrt{1260}=\sqrt{36*35}=\sqrt{36}*\sqrt{35}=6\sqrt{35}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-6\sqrt{35}}{2*5}=\frac{-30-6\sqrt{35}}{10}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+6\sqrt{35}}{2*5}=\frac{-30+6\sqrt{35}}{10}
$