x^2+100x+500=1000

Solution for x^2+100x+500=1000 equation:

x^2+100x+500=1000

We move all terms to the left:

x^2+100x+500-(1000)=0

We add all the numbers together, and all the variables

x^2+100x-500=0

a = 1; b = 100; c = -500;
Δ = b2-4ac
Δ = 1002-4·1·(-500)
Δ = 12000
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:

$\sqrt{\Delta}=\sqrt{12000}=\sqrt{400*30}=\sqrt{400}*\sqrt{30}=20\sqrt{30}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(100)-20\sqrt{30}}{2*1}=\frac{-100-20\sqrt{30}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(100)+20\sqrt{30}}{2*1}=\frac{-100+20\sqrt{30}}{2}
$