(5n+7)(n-1)=0

Solution for (5n+7)(n-1)=0 equation:

(5n+7)(n-1)=0

We multiply parentheses ..

(+5n^2-5n+7n-7)=0

We get rid of parentheses

5n^2-5n+7n-7=0

We add all the numbers together, and all the variables

5n^2+2n-7=0

a = 5; b = 2; c = -7;
Δ = b2-4ac
Δ = 22-4·5·(-7)
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-12}{2*5}=\frac{-14}{10}
=-1+2/5
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+12}{2*5}=\frac{10}{10}
=1
$