200=-0.5x^2+100x-60

Solution for 200=-0.5x^2+100x-60 equation:

200=-0.5x^2+100x-60

We move all terms to the left:

200-(-0.5x^2+100x-60)=0

We get rid of parentheses

0.5x^2-100x+60+200=0

We add all the numbers together, and all the variables

0.5x^2-100x+260=0

a = 0.5; b = -100; c = +260;
Δ = b2-4ac
Δ = -1002-4·0.5·260
Δ = 9480
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:

$\sqrt{\Delta}=\sqrt{9480}=\sqrt{4*2370}=\sqrt{4}*\sqrt{2370}=2\sqrt{2370}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-100)-2\sqrt{2370}}{2*0.5}=\frac{100-2\sqrt{2370}}{1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-100)+2\sqrt{2370}}{2*0.5}=\frac{100+2\sqrt{2370}}{1}
$