6n(n-7)=30

Solution for 6n(n-7)=30 equation:

6n(n-7)=30

We move all terms to the left:

6n(n-7)-(30)=0

We multiply parentheses

6n^2-42n-30=0

a = 6; b = -42; c = -30;
Δ = b2-4ac
Δ = -422-4·6·(-30)
Δ = 2484
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:

$\sqrt{\Delta}=\sqrt{2484}=\sqrt{36*69}=\sqrt{36}*\sqrt{69}=6\sqrt{69}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-6\sqrt{69}}{2*6}=\frac{42-6\sqrt{69}}{12}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+6\sqrt{69}}{2*6}=\frac{42+6\sqrt{69}}{12}
$