-3(2n-7)4n=15

Solution for -3(2n-7)4n=15 equation:

-3(2n-7)4n=15

We move all terms to the left:

-3(2n-7)4n-(15)=0

We multiply parentheses

-24n^2+84n-15=0

a = -24; b = 84; c = -15;
Δ = b2-4ac
Δ = 842-4·(-24)·(-15)
Δ = 5616
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:

$\sqrt{\Delta}=\sqrt{5616}=\sqrt{144*39}=\sqrt{144}*\sqrt{39}=12\sqrt{39}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(84)-12\sqrt{39}}{2*-24}=\frac{-84-12\sqrt{39}}{-48}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(84)+12\sqrt{39}}{2*-24}=\frac{-84+12\sqrt{39}}{-48}
$