b(-18-b)=-24

Solution for b(-18-b)=-24 equation:

b(-18-b)=-24

We move all terms to the left:

b(-18-b)-(-24)=0

We add all the numbers together, and all the variables

b(-1b-18)-(-24)=0

We add all the numbers together, and all the variables

b(-1b-18)+24=0

We multiply parentheses

-1b^2-18b+24=0

a = -1; b = -18; c = +24;
Δ = b2-4ac
Δ = -182-4·(-1)·24
Δ = 420
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:

$\sqrt{\Delta}=\sqrt{420}=\sqrt{4*105}=\sqrt{4}*\sqrt{105}=2\sqrt{105}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{105}}{2*-1}=\frac{18-2\sqrt{105}}{-2}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{105}}{2*-1}=\frac{18+2\sqrt{105}}{-2}
$