-2x^2+260x-5000=0

Solution for -2x^2+260x-5000=0 equation:

-2x^2+260x-5000=0

a = -2; b = 260; c = -5000;
Δ = b2-4ac
Δ = 2602-4·(-2)·(-5000)
Δ = 27600
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:

$\sqrt{\Delta}=\sqrt{27600}=\sqrt{400*69}=\sqrt{400}*\sqrt{69}=20\sqrt{69}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(260)-20\sqrt{69}}{2*-2}=\frac{-260-20\sqrt{69}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(260)+20\sqrt{69}}{2*-2}=\frac{-260+20\sqrt{69}}{-4}
$