6n(4+5n)=7

Solution for 6n(4+5n)=7 equation:

6n(4+5n)=7

We move all terms to the left:

6n(4+5n)-(7)=0

We add all the numbers together, and all the variables

6n(5n+4)-7=0

We multiply parentheses

30n^2+24n-7=0

a = 30; b = 24; c = -7;
Δ = b2-4ac
Δ = 242-4·30·(-7)
Δ = 1416
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:

$\sqrt{\Delta}=\sqrt{1416}=\sqrt{4*354}=\sqrt{4}*\sqrt{354}=2\sqrt{354}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-2\sqrt{354}}{2*30}=\frac{-24-2\sqrt{354}}{60}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+2\sqrt{354}}{2*30}=\frac{-24+2\sqrt{354}}{60}
$