7b(b-4)-11(b-4)=0

Solution for 7b(b-4)-11(b-4)=0 equation:

7b(b-4)-11(b-4)=0

We multiply parentheses

7b^2-28b-11b+44=0

We add all the numbers together, and all the variables

7b^2-39b+44=0

a = 7; b = -39; c = +44;
Δ = b2-4ac
Δ = -392-4·7·44
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-39)-17}{2*7}=\frac{22}{14}
=1+4/7
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-39)+17}{2*7}=\frac{56}{14}
=4
$