9w^2-76=0

Solution for 9w^2-76=0 equation:

9w^2-76=0

a = 9; b = 0; c = -76;
Δ = b2-4ac
Δ = 02-4·9·(-76)
Δ = 2736
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:

$\sqrt{\Delta}=\sqrt{2736}=\sqrt{144*19}=\sqrt{144}*\sqrt{19}=12\sqrt{19}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{19}}{2*9}=\frac{0-12\sqrt{19}}{18}
=-\frac{12\sqrt{19}}{18}
=-\frac{2\sqrt{19}}{3}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{19}}{2*9}=\frac{0+12\sqrt{19}}{18}
=\frac{12\sqrt{19}}{18}
=\frac{2\sqrt{19}}{3}
$