(x)=-5x^2+200

Solution for (x)=-5x^2+200 equation:

(x)=-5x^2+200

We move all terms to the left:

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

We get rid of parentheses

5x^2+x-200=0

a = 5; b = 1; c = -200;
Δ = b2-4ac
Δ = 12-4·5·(-200)
Δ = 4001
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{4001}}{2*5}=\frac{-1-\sqrt{4001}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{4001}}{2*5}=\frac{-1+\sqrt{4001}}{10}
$