-w^2=-596

Solution for -w^2=-596 equation:

-w^2=-596

We move all terms to the left:

-w^2-(-596)=0

We add all the numbers together, and all the variables

-1w^2+596=0

a = -1; b = 0; c = +596;
Δ = b2-4ac
Δ = 02-4·(-1)·596
Δ = 2384
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:

$\sqrt{\Delta}=\sqrt{2384}=\sqrt{16*149}=\sqrt{16}*\sqrt{149}=4\sqrt{149}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{149}}{2*-1}=\frac{0-4\sqrt{149}}{-2}
=-\frac{4\sqrt{149}}{-2}
=-\frac{2\sqrt{149}}{-1}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{149}}{2*-1}=\frac{0+4\sqrt{149}}{-2}
=\frac{4\sqrt{149}}{-2}
=\frac{2\sqrt{149}}{-1}
$