(x)=-5x2+1000x+500

Solution for (x)=-5x2+1000x+500 equation:

(x)=-5x^2+1000x+500

We move all terms to the left:

(x)-(-5x^2+1000x+500)=0

We get rid of parentheses

5x^2-1000x+x-500=0

We add all the numbers together, and all the variables

5x^2-999x-500=0

a = 5; b = -999; c = -500;
Δ = b2-4ac
Δ = -9992-4·5·(-500)
Δ = 1008001
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{-(-999)-\sqrt{1008001}}{2*5}=\frac{999-\sqrt{1008001}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-999)+\sqrt{1008001}}{2*5}=\frac{999+\sqrt{1008001}}{10}
$