w^2-2w-85=0

Solution for w^2-2w-85=0 equation:

w^2-2w-85=0

a = 1; b = -2; c = -85;
Δ = b2-4ac
Δ = -22-4·1·(-85)
Δ = 344
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:

$\sqrt{\Delta}=\sqrt{344}=\sqrt{4*86}=\sqrt{4}*\sqrt{86}=2\sqrt{86}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{86}}{2*1}=\frac{2-2\sqrt{86}}{2}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{86}}{2*1}=\frac{2+2\sqrt{86}}{2}
$