(4d-7)(8d-16)=0

Solution for (4d-7)(8d-16)=0 equation:

(4d-7)(8d-16)=0

We multiply parentheses ..

(+32d^2-64d-56d+112)=0

We get rid of parentheses

32d^2-64d-56d+112=0

We add all the numbers together, and all the variables

32d^2-120d+112=0

a = 32; b = -120; c = +112;
Δ = b2-4ac
Δ = -1202-4·32·112
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-120)-8}{2*32}=\frac{112}{64}
=1+3/4
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-120)+8}{2*32}=\frac{128}{64}
=2
$