6n(2n+5)=66

Solution for 6n(2n+5)=66 equation:

6n(2n+5)=66

We move all terms to the left:

6n(2n+5)-(66)=0

We multiply parentheses

12n^2+30n-66=0

a = 12; b = 30; c = -66;
Δ = b2-4ac
Δ = 302-4·12·(-66)
Δ = 4068
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:

$\sqrt{\Delta}=\sqrt{4068}=\sqrt{36*113}=\sqrt{36}*\sqrt{113}=6\sqrt{113}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-6\sqrt{113}}{2*12}=\frac{-30-6\sqrt{113}}{24}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+6\sqrt{113}}{2*12}=\frac{-30+6\sqrt{113}}{24}
$