-23w^2=-213

Solution for -23w^2=-213 equation:

-23w^2=-213

We move all terms to the left:

-23w^2-(-213)=0

We add all the numbers together, and all the variables

-23w^2+213=0

a = -23; b = 0; c = +213;
Δ = b2-4ac
Δ = 02-4·(-23)·213
Δ = 19596
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:

$\sqrt{\Delta}=\sqrt{19596}=\sqrt{4*4899}=\sqrt{4}*\sqrt{4899}=2\sqrt{4899}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{4899}}{2*-23}=\frac{0-2\sqrt{4899}}{-46}
=-\frac{2\sqrt{4899}}{-46}
=-\frac{\sqrt{4899}}{-23}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{4899}}{2*-23}=\frac{0+2\sqrt{4899}}{-46}
=\frac{2\sqrt{4899}}{-46}
=\frac{\sqrt{4899}}{-23}
$