0=200-10x-5x^2

Solution for 0=200-10x-5x^2 equation:

0=200-10x-5x^2

We move all terms to the left:

0-(200-10x-5x^2)=0

We add all the numbers together, and all the variables

-(200-10x-5x^2)=0

We get rid of parentheses

5x^2+10x-200=0

a = 5; b = 10; c = -200;
Δ = b2-4ac
Δ = 102-4·5·(-200)
Δ = 4100
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:

$\sqrt{\Delta}=\sqrt{4100}=\sqrt{100*41}=\sqrt{100}*\sqrt{41}=10\sqrt{41}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-10\sqrt{41}}{2*5}=\frac{-10-10\sqrt{41}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+10\sqrt{41}}{2*5}=\frac{-10+10\sqrt{41}}{10}
$