4b=72-b2

Solution for 4b=72-b2 equation:

4b=72-b2

We move all terms to the left:

4b-(72-b2)=0

We add all the numbers together, and all the variables

-(-1b^2+72)+4b=0

We get rid of parentheses

1b^2+4b-72=0

We add all the numbers together, and all the variables

b^2+4b-72=0

a = 1; b = 4; c = -72;
Δ = b2-4ac
Δ = 42-4·1·(-72)
Δ = 304
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:

$\sqrt{\Delta}=\sqrt{304}=\sqrt{16*19}=\sqrt{16}*\sqrt{19}=4\sqrt{19}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{19}}{2*1}=\frac{-4-4\sqrt{19}}{2}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{19}}{2*1}=\frac{-4+4\sqrt{19}}{2}
$