102=2x^2+48(x)

Solution for 102=2x^2+48(x) equation:

102=2x^2+48(x)

We move all terms to the left:

102-(2x^2+48(x))=0

We get rid of parentheses

-2x^2-48x+102=0

a = -2; b = -48; c = +102;
Δ = b2-4ac
Δ = -482-4·(-2)·102
Δ = 3120
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:

$\sqrt{\Delta}=\sqrt{3120}=\sqrt{16*195}=\sqrt{16}*\sqrt{195}=4\sqrt{195}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-4\sqrt{195}}{2*-2}=\frac{48-4\sqrt{195}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+4\sqrt{195}}{2*-2}=\frac{48+4\sqrt{195}}{-4}
$