w^2=91

Solution for w^2=91 equation:

w^2=91

We move all terms to the left:

w^2-(91)=0

a = 1; b = 0; c = -91;
Δ = b2-4ac
Δ = 02-4·1·(-91)
Δ = 364
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:

$\sqrt{\Delta}=\sqrt{364}=\sqrt{4*91}=\sqrt{4}*\sqrt{91}=2\sqrt{91}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{91}}{2*1}=\frac{0-2\sqrt{91}}{2}
=-\frac{2\sqrt{91}}{2}
=-\sqrt{91}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{91}}{2*1}=\frac{0+2\sqrt{91}}{2}
=\frac{2\sqrt{91}}{2}
=\sqrt{91}
$