(4b-7)(4b-1)=0

Solution for (4b-7)(4b-1)=0 equation:

(4b-7)(4b-1)=0

We multiply parentheses ..

(+16b^2-4b-28b+7)=0

We get rid of parentheses

16b^2-4b-28b+7=0

We add all the numbers together, and all the variables

16b^2-32b+7=0

a = 16; b = -32; c = +7;
Δ = b2-4ac
Δ = -322-4·16·7
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-24}{2*16}=\frac{8}{32}
=1/4
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+24}{2*16}=\frac{56}{32}
=1+3/4
$