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

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

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

We multiply parentheses ..

(+5n^2+8n-35n-56)=0

We get rid of parentheses

5n^2+8n-35n-56=0

We add all the numbers together, and all the variables

5n^2-27n-56=0

a = 5; b = -27; c = -56;
Δ = b2-4ac
Δ = -272-4·5·(-56)
Δ = 1849
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1849}=43$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-43}{2*5}=\frac{-16}{10}
=-1+3/5
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+43}{2*5}=\frac{70}{10}
=7
$