8x^2=384+16x

Solution for 8x^2=384+16x equation:

8x^2=384+16x

We move all terms to the left:

8x^2-(384+16x)=0

We add all the numbers together, and all the variables

8x^2-(16x+384)=0

We get rid of parentheses

8x^2-16x-384=0

a = 8; b = -16; c = -384;
Δ = b2-4ac
Δ = -162-4·8·(-384)
Δ = 12544
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{12544}=112$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-112}{2*8}=\frac{-96}{16}
=-6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+112}{2*8}=\frac{128}{16}
=8
$