(-7n+8)(5n-5)=0

Solution for (-7n+8)(5n-5)=0 equation:

(-7n+8)(5n-5)=0

We multiply parentheses ..

(-35n^2+35n+40n-40)=0

We get rid of parentheses

-35n^2+35n+40n-40=0

We add all the numbers together, and all the variables

-35n^2+75n-40=0

a = -35; b = 75; c = -40;
Δ = b2-4ac
Δ = 752-4·(-35)·(-40)
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(75)-5}{2*-35}=\frac{-80}{-70}
=1+1/7
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(75)+5}{2*-35}=\frac{-70}{-70}
=1
$