-.5x^2-36x-310=0

Solution for -.5x^2-36x-310=0 equation:

-.5x^2-36x-310=0

We add all the numbers together, and all the variables

-0.5x^2-36x-310=0

a = -0.5; b = -36; c = -310;
Δ = b2-4ac
Δ = -362-4·(-0.5)·(-310)
Δ = 676
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{676}=26$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-26}{2*-0.5}=\frac{10}{-1}
=-10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+26}{2*-0.5}=\frac{62}{-1}
=-62
$