8(x-1)(x-6)=0

Solution for 8(x-1)(x-6)=0 equation:

8(x-1)(x-6)=0

We multiply parentheses ..

8(+x^2-6x-1x+6)=0

We multiply parentheses

8x^2-48x-8x+48=0

We add all the numbers together, and all the variables

8x^2-56x+48=0

a = 8; b = -56; c = +48;
Δ = b2-4ac
Δ = -562-4·8·48
Δ = 1600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1600}=40$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-56)-40}{2*8}=\frac{16}{16}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-56)+40}{2*8}=\frac{96}{16}
=6
$