8b^2=224+24b

Solution for 8b^2=224+24b equation:

8b^2=224+24b

We move all terms to the left:

8b^2-(224+24b)=0

We add all the numbers together, and all the variables

8b^2-(24b+224)=0

We get rid of parentheses

8b^2-24b-224=0

a = 8; b = -24; c = -224;
Δ = b2-4ac
Δ = -242-4·8·(-224)
Δ = 7744
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{7744}=88$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-88}{2*8}=\frac{-64}{16}
=-4
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+88}{2*8}=\frac{112}{16}
=7
$