5(2n2-5n-3)=0

Solution for 5(2n2-5n-3)=0 equation:

5(2n^2-5n-3)=0

We multiply parentheses

10n^2-25n-15=0

a = 10; b = -25; c = -15;
Δ = b2-4ac
Δ = -252-4·10·(-15)
Δ = 1225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1225}=35$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-25)-35}{2*10}=\frac{-10}{20}
=-1/2
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+35}{2*10}=\frac{60}{20}
=3
$