-13x^2+1690x-52000=0

Solution for -13x^2+1690x-52000=0 equation:

-13x^2+1690x-52000=0

a = -13; b = 1690; c = -52000;
Δ = b2-4ac
Δ = 16902-4·(-13)·(-52000)
Δ = 152100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{152100}=390$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1690)-390}{2*-13}=\frac{-2080}{-26}
=+80
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1690)+390}{2*-13}=\frac{-1300}{-26}
=+50
$