(x^2+10x-500)=0

Solution for (x^2+10x-500)=0 equation:

(x^2+10x-500)=0

We get rid of parentheses

x^2+10x-500=0

a = 1; b = 10; c = -500;
Δ = b2-4ac
Δ = 102-4·1·(-500)
Δ = 2100
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:

$\sqrt{\Delta}=\sqrt{2100}=\sqrt{100*21}=\sqrt{100}*\sqrt{21}=10\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-10\sqrt{21}}{2*1}=\frac{-10-10\sqrt{21}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+10\sqrt{21}}{2*1}=\frac{-10+10\sqrt{21}}{2}
$