x^2+1686x+709771=0

Solution for x^2+1686x+709771=0 equation:

x^2+1686x+709771=0

a = 1; b = 1686; c = +709771;
Δ = b2-4ac
Δ = 16862-4·1·709771
Δ = 3512
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:

$\sqrt{\Delta}=\sqrt{3512}=\sqrt{4*878}=\sqrt{4}*\sqrt{878}=2\sqrt{878}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1686)-2\sqrt{878}}{2*1}=\frac{-1686-2\sqrt{878}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1686)+2\sqrt{878}}{2*1}=\frac{-1686+2\sqrt{878}}{2}
$