-0.5x^2-50x-150=0

Solution for -0.5x^2-50x-150=0 equation:

-0.5x^2-50x-150=0

a = -0.5; b = -50; c = -150;
Δ = b2-4ac
Δ = -502-4·(-0.5)·(-150)
Δ = 2200
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:

$\sqrt{\Delta}=\sqrt{2200}=\sqrt{100*22}=\sqrt{100}*\sqrt{22}=10\sqrt{22}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-10\sqrt{22}}{2*-0.5}=\frac{50-10\sqrt{22}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+10\sqrt{22}}{2*-0.5}=\frac{50+10\sqrt{22}}{-1}
$