(2n-1)(5n+6)=0

Solution for (2n-1)(5n+6)=0 equation:

(2n-1)(5n+6)=0

We multiply parentheses ..

(+10n^2+12n-5n-6)=0

We get rid of parentheses

10n^2+12n-5n-6=0

We add all the numbers together, and all the variables

10n^2+7n-6=0

a = 10; b = 7; c = -6;
Δ = b2-4ac
Δ = 72-4·10·(-6)
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-17}{2*10}=\frac{-24}{20}
=-1+1/5
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+17}{2*10}=\frac{10}{20}
=1/2
$