0=-0.5x^2+10x+150

Solution for 0=-0.5x^2+10x+150 equation:

0=-0.5x^2+10x+150

We move all terms to the left:

0-(-0.5x^2+10x+150)=0

We add all the numbers together, and all the variables

-(-0.5x^2+10x+150)=0

We get rid of parentheses

0.5x^2-10x-150=0

a = 0.5; b = -10; c = -150;
Δ = b2-4ac
Δ = -102-4·0.5·(-150)
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-20}{2*0.5}=\frac{-10}{1}
=-10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+20}{2*0.5}=\frac{30}{1}
=30
$