31w=-w^2

Solution for 31w=-w^2 equation:

31w=-w^2

We move all terms to the left:

31w-(-w^2)=0

We get rid of parentheses

w^2+31w=0

a = 1; b = 31; c = 0;
Δ = b2-4ac
Δ = 312-4·1·0
Δ = 961
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{961}=31$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(31)-31}{2*1}=\frac{-62}{2}
=-31
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(31)+31}{2*1}=\frac{0}{2}
=0
$