48=16x^2+48x

Solution for 48=16x^2+48x equation:

48=16x^2+48x

We move all terms to the left:

48-(16x^2+48x)=0

We get rid of parentheses

-16x^2-48x+48=0

a = -16; b = -48; c = +48;
Δ = b2-4ac
Δ = -482-4·(-16)·48
Δ = 5376
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{5376}=\sqrt{256*21}=\sqrt{256}*\sqrt{21}=16\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-16\sqrt{21}}{2*-16}=\frac{48-16\sqrt{21}}{-32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+16\sqrt{21}}{2*-16}=\frac{48+16\sqrt{21}}{-32}
$