0=-0.5x^2-350x

Solution for 0=-0.5x^2-350x equation:

0=-0.5x^2-350x

We move all terms to the left:

0-(-0.5x^2-350x)=0

We add all the numbers together, and all the variables

-(-0.5x^2-350x)=0

We get rid of parentheses

0.5x^2+350x=0

a = 0.5; b = 350; c = 0;
Δ = b2-4ac
Δ = 3502-4·0.5·0
Δ = 122500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{122500}=350$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(350)-350}{2*0.5}=\frac{-700}{1}
=-700
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(350)+350}{2*0.5}=\frac{0}{1}
=0
$