X^2-2x-185=0

Solution for X^2-2x-185=0 equation:

X^2-2X-185=0

a = 1; b = -2; c = -185;
Δ = b2-4ac
Δ = -22-4·1·(-185)
Δ = 744
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:

$\sqrt{\Delta}=\sqrt{744}=\sqrt{4*186}=\sqrt{4}*\sqrt{186}=2\sqrt{186}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{186}}{2*1}=\frac{2-2\sqrt{186}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{186}}{2*1}=\frac{2+2\sqrt{186}}{2}
$