5(w-1)(w-7)=1

Solution for 5(w-1)(w-7)=1 equation:

5(w-1)(w-7)=1

We move all terms to the left:

5(w-1)(w-7)-(1)=0

We multiply parentheses ..

5(+w^2-7w-1w+7)-1=0

We multiply parentheses

5w^2-35w-5w+35-1=0

We add all the numbers together, and all the variables

5w^2-40w+34=0

a = 5; b = -40; c = +34;
Δ = b2-4ac
Δ = -402-4·5·34
Δ = 920
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{920}=\sqrt{4*230}=\sqrt{4}*\sqrt{230}=2\sqrt{230}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-2\sqrt{230}}{2*5}=\frac{40-2\sqrt{230}}{10}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+2\sqrt{230}}{2*5}=\frac{40+2\sqrt{230}}{10}
$