320=-3.5n^2+140n-1024

Solution for 320=-3.5n^2+140n-1024 equation:

320=-3.5n^2+140n-1024

We move all terms to the left:

320-(-3.5n^2+140n-1024)=0

We get rid of parentheses

3.5n^2-140n+1024+320=0

We add all the numbers together, and all the variables

3.5n^2-140n+1344=0

a = 3.5; b = -140; c = +1344;
Δ = b2-4ac
Δ = -1402-4·3.5·1344
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-140)-28}{2*3.5}=\frac{112}{7}
=16
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-140)+28}{2*3.5}=\frac{168}{7}
=24
$