(5n-3)(2n+7)=0

Solution for (5n-3)(2n+7)=0 equation:

(5n-3)(2n+7)=0

We multiply parentheses ..

(+10n^2+35n-6n-21)=0

We get rid of parentheses

10n^2+35n-6n-21=0

We add all the numbers together, and all the variables

10n^2+29n-21=0

a = 10; b = 29; c = -21;
Δ = b2-4ac
Δ = 292-4·10·(-21)
Δ = 1681
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1681}=41$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(29)-41}{2*10}=\frac{-70}{20}
=-3+1/2
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(29)+41}{2*10}=\frac{12}{20}
=3/5
$