50=0.5x^2-40x-600

Solution for 50=0.5x^2-40x-600 equation:

50=0.5x^2-40x-600

We move all terms to the left:

50-(0.5x^2-40x-600)=0

We get rid of parentheses

-0.5x^2+40x+600+50=0

We add all the numbers together, and all the variables

-0.5x^2+40x+650=0

a = -0.5; b = 40; c = +650;
Δ = b2-4ac
Δ = 402-4·(-0.5)·650
Δ = 2900
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:

$\sqrt{\Delta}=\sqrt{2900}=\sqrt{100*29}=\sqrt{100}*\sqrt{29}=10\sqrt{29}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-10\sqrt{29}}{2*-0.5}=\frac{-40-10\sqrt{29}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+10\sqrt{29}}{2*-0.5}=\frac{-40+10\sqrt{29}}{-1}
$