-2x^2+48x-254=0

Solution for -2x^2+48x-254=0 equation:

-2x^2+48x-254=0

a = -2; b = 48; c = -254;
Δ = b2-4ac
Δ = 482-4·(-2)·(-254)
Δ = 272
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:

$\sqrt{\Delta}=\sqrt{272}=\sqrt{16*17}=\sqrt{16}*\sqrt{17}=4\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-4\sqrt{17}}{2*-2}=\frac{-48-4\sqrt{17}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+4\sqrt{17}}{2*-2}=\frac{-48+4\sqrt{17}}{-4}
$