1018=2x^2-48x

Solution for 1018=2x^2-48x equation:

1018=2x^2-48x

We move all terms to the left:

1018-(2x^2-48x)=0

We get rid of parentheses

-2x^2+48x+1018=0

a = -2; b = 48; c = +1018;
Δ = b2-4ac
Δ = 482-4·(-2)·1018
Δ = 10448
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:

$\sqrt{\Delta}=\sqrt{10448}=\sqrt{16*653}=\sqrt{16}*\sqrt{653}=4\sqrt{653}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-4\sqrt{653}}{2*-2}=\frac{-48-4\sqrt{653}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+4\sqrt{653}}{2*-2}=\frac{-48+4\sqrt{653}}{-4}
$