32n^2+56n=4

Solution for 32n^2+56n=4 equation:

32n^2+56n=4

We move all terms to the left:

32n^2+56n-(4)=0

a = 32; b = 56; c = -4;
Δ = b2-4ac
Δ = 562-4·32·(-4)
Δ = 3648
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:

$\sqrt{\Delta}=\sqrt{3648}=\sqrt{64*57}=\sqrt{64}*\sqrt{57}=8\sqrt{57}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(56)-8\sqrt{57}}{2*32}=\frac{-56-8\sqrt{57}}{64}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(56)+8\sqrt{57}}{2*32}=\frac{-56+8\sqrt{57}}{64}
$