(5n-4)(n-7)=0

Solution for (5n-4)(n-7)=0 equation:

(5n-4)(n-7)=0

We multiply parentheses ..

(+5n^2-35n-4n+28)=0

We get rid of parentheses

5n^2-35n-4n+28=0

We add all the numbers together, and all the variables

5n^2-39n+28=0

a = 5; b = -39; c = +28;
Δ = b2-4ac
Δ = -392-4·5·28
Δ = 961
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{961}=31$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-39)-31}{2*5}=\frac{8}{10}
=4/5
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-39)+31}{2*5}=\frac{70}{10}
=7
$