(q-8)(5q-2)=0

Solution for (q-8)(5q-2)=0 equation:

(q-8)(5q-2)=0

We multiply parentheses ..

(+5q^2-2q-40q+16)=0

We get rid of parentheses

5q^2-2q-40q+16=0

We add all the numbers together, and all the variables

5q^2-42q+16=0

a = 5; b = -42; c = +16;
Δ = b2-4ac
Δ = -422-4·5·16
Δ = 1444
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1444}=38$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-38}{2*5}=\frac{4}{10}
=2/5
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+38}{2*5}=\frac{80}{10}
=8
$