3840=8x+4x^2

Solution for 3840=8x+4x^2 equation:

3840=8x+4x^2

We move all terms to the left:

3840-(8x+4x^2)=0

We get rid of parentheses

-4x^2-8x+3840=0

a = -4; b = -8; c = +3840;
Δ = b2-4ac
Δ = -82-4·(-4)·3840
Δ = 61504
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{61504}=248$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-248}{2*-4}=\frac{-240}{-8}
=+30
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+248}{2*-4}=\frac{256}{-8}
=-32
$