(2n-1)(5n+3)=0

Solution for (2n-1)(5n+3)=0 equation:

(2n-1)(5n+3)=0

We multiply parentheses ..

(+10n^2+6n-5n-3)=0

We get rid of parentheses

10n^2+6n-5n-3=0

We add all the numbers together, and all the variables

10n^2+n-3=0

a = 10; b = 1; c = -3;
Δ = b2-4ac
Δ = 12-4·10·(-3)
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-11}{2*10}=\frac{-12}{20}
=-3/5
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+11}{2*10}=\frac{10}{20}
=1/2
$