w^2-662w-9612=0

Solution for w^2-662w-9612=0 equation:

w^2-662w-9612=0

a = 1; b = -662; c = -9612;
Δ = b2-4ac
Δ = -6622-4·1·(-9612)
Δ = 476692
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:

$\sqrt{\Delta}=\sqrt{476692}=\sqrt{4*119173}=\sqrt{4}*\sqrt{119173}=2\sqrt{119173}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-662)-2\sqrt{119173}}{2*1}=\frac{662-2\sqrt{119173}}{2}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-662)+2\sqrt{119173}}{2*1}=\frac{662+2\sqrt{119173}}{2}
$