(7a-4)(4a-8)=0

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

(7a-4)(4a-8)=0

We multiply parentheses ..

(+28a^2-56a-16a+32)=0

We get rid of parentheses

28a^2-56a-16a+32=0

We add all the numbers together, and all the variables

28a^2-72a+32=0

a = 28; b = -72; c = +32;
Δ = b2-4ac
Δ = -722-4·28·32
Δ = 1600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1600}=40$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-72)-40}{2*28}=\frac{32}{56}
=4/7
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-72)+40}{2*28}=\frac{112}{56}
=2
$