0.5w^2+6w=186624

Solution for 0.5w^2+6w=186624 equation:

0.5w^2+6w=186624

We move all terms to the left:

0.5w^2+6w-(186624)=0

a = 0.5; b = 6; c = -186624;
Δ = b2-4ac
Δ = 62-4·0.5·(-186624)
Δ = 373284
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:

$\sqrt{\Delta}=\sqrt{373284}=\sqrt{36*10369}=\sqrt{36}*\sqrt{10369}=6\sqrt{10369}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6\sqrt{10369}}{2*0.5}=\frac{-6-6\sqrt{10369}}{1}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6\sqrt{10369}}{2*0.5}=\frac{-6+6\sqrt{10369}}{1}
$