7b^2+9=24b

Solution for 7b^2+9=24b equation:

7b^2+9=24b

We move all terms to the left:

7b^2+9-(24b)=0

a = 7; b = -24; c = +9;
Δ = b2-4ac
Δ = -242-4·7·9
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-18}{2*7}=\frac{6}{14}
=3/7
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+18}{2*7}=\frac{42}{14}
=3
$