3n(5n-6)=10

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

3n(5n-6)=10

We move all terms to the left:

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

We multiply parentheses

15n^2-18n-10=0

a = 15; b = -18; c = -10;
Δ = b2-4ac
Δ = -182-4·15·(-10)
Δ = 924
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{924}=\sqrt{4*231}=\sqrt{4}*\sqrt{231}=2\sqrt{231}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{231}}{2*15}=\frac{18-2\sqrt{231}}{30}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{231}}{2*15}=\frac{18+2\sqrt{231}}{30}
$