2b(b-4)=72

Solution for 2b(b-4)=72 equation:

2b(b-4)=72

We move all terms to the left:

2b(b-4)-(72)=0

We multiply parentheses

2b^2-8b-72=0

a = 2; b = -8; c = -72;
Δ = b2-4ac
Δ = -82-4·2·(-72)
Δ = 640
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:

$\sqrt{\Delta}=\sqrt{640}=\sqrt{64*10}=\sqrt{64}*\sqrt{10}=8\sqrt{10}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-8\sqrt{10}}{2*2}=\frac{8-8\sqrt{10}}{4}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+8\sqrt{10}}{2*2}=\frac{8+8\sqrt{10}}{4}
$