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

Solution for (6n^2-10n-10)-(3n^2-5n-10)=0 equation:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

3n^2-5n=0

a = 3; b = -5; c = 0;
Δ = b2-4ac
Δ = -52-4·3·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5}{2*3}=\frac{0}{6}
=0
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5}{2*3}=\frac{10}{6}
=1+2/3
$