-5n(4n-2.4)+2(1.3+6n)=-5.4

Solution for -5n(4n-2.4)+2(1.3+6n)=-5.4 equation:

-5n(4n-2.4)+2(1.3+6n)=-5.4

We move all terms to the left:

-5n(4n-2.4)+2(1.3+6n)-(-5.4)=0

We add all the numbers together, and all the variables

-5n(4n-2.4)+2(6n+1.3)-(-5.4)=0

We add all the numbers together, and all the variables

-5n(4n-2.4)+2(6n+1.3)+5.4=0

We multiply parentheses

-20n^2+12n+12n+2.6+5.4=0

We add all the numbers together, and all the variables

-20n^2+24n+8=0

a = -20; b = 24; c = +8;
Δ = b2-4ac
Δ = 242-4·(-20)·8
Δ = 1216
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:

$\sqrt{\Delta}=\sqrt{1216}=\sqrt{64*19}=\sqrt{64}*\sqrt{19}=8\sqrt{19}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-8\sqrt{19}}{2*-20}=\frac{-24-8\sqrt{19}}{-40}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+8\sqrt{19}}{2*-20}=\frac{-24+8\sqrt{19}}{-40}
$