5b^2+16=-24b

Solution for 5b^2+16=-24b equation:

5b^2+16=-24b

We move all terms to the left:

5b^2+16-(-24b)=0

We get rid of parentheses

5b^2+24b+16=0

a = 5; b = 24; c = +16;
Δ = b2-4ac
Δ = 242-4·5·16
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-16}{2*5}=\frac{-40}{10}
=-4
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+16}{2*5}=\frac{-8}{10}
=-4/5
$