w^2+2w-1250=0

Solution for w^2+2w-1250=0 equation:

w^2+2w-1250=0

a = 1; b = 2; c = -1250;
Δ = b2-4ac
Δ = 22-4·1·(-1250)
Δ = 5004
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{5004}=\sqrt{36*139}=\sqrt{36}*\sqrt{139}=6\sqrt{139}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-6\sqrt{139}}{2*1}=\frac{-2-6\sqrt{139}}{2}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+6\sqrt{139}}{2*1}=\frac{-2+6\sqrt{139}}{2}
$