2w^2+12w-2773=0

Solution for 2w^2+12w-2773=0 equation:

2w^2+12w-2773=0

a = 2; b = 12; c = -2773;
Δ = b2-4ac
Δ = 122-4·2·(-2773)
Δ = 22328
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:

$\sqrt{\Delta}=\sqrt{22328}=\sqrt{4*5582}=\sqrt{4}*\sqrt{5582}=2\sqrt{5582}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-2\sqrt{5582}}{2*2}=\frac{-12-2\sqrt{5582}}{4}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+2\sqrt{5582}}{2*2}=\frac{-12+2\sqrt{5582}}{4}
$