(x-8)(5x-1)=0

Solution for (x-8)(5x-1)=0 equation:

(x-8)(5x-1)=0

We multiply parentheses ..

(+5x^2-1x-40x+8)=0

We get rid of parentheses

5x^2-1x-40x+8=0

We add all the numbers together, and all the variables

5x^2-41x+8=0

a = 5; b = -41; c = +8;
Δ = b2-4ac
Δ = -412-4·5·8
Δ = 1521
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1521}=39$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-41)-39}{2*5}=\frac{2}{10}
=1/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-41)+39}{2*5}=\frac{80}{10}
=8
$