650x-0.1x^2-50000=0

Solution for 650x-0.1x^2-50000=0 equation:

650x-0.1x^2-50000=0

a = -0.1; b = 650; c = -50000;
Δ = b2-4ac
Δ = 6502-4·(-0.1)·(-50000)
Δ = 402500
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:

$\sqrt{\Delta}=\sqrt{402500}=\sqrt{2500*161}=\sqrt{2500}*\sqrt{161}=50\sqrt{161}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(650)-50\sqrt{161}}{2*-0.1}=\frac{-650-50\sqrt{161}}{-0.2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(650)+50\sqrt{161}}{2*-0.1}=\frac{-650+50\sqrt{161}}{-0.2}
$