-2x^2+100x-300=0

Solution for -2x^2+100x-300=0 equation:

-2x^2+100x-300=0

a = -2; b = 100; c = -300;
Δ = b2-4ac
Δ = 1002-4·(-2)·(-300)
Δ = 7600
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:

$\sqrt{\Delta}=\sqrt{7600}=\sqrt{400*19}=\sqrt{400}*\sqrt{19}=20\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(100)-20\sqrt{19}}{2*-2}=\frac{-100-20\sqrt{19}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(100)+20\sqrt{19}}{2*-2}=\frac{-100+20\sqrt{19}}{-4}
$