3w*w=306

Solution for 3w*w=306 equation:

3w*w=306

We move all terms to the left:

3w*w-(306)=0

Wy multiply elements

3w^2-306=0

a = 3; b = 0; c = -306;
Δ = b2-4ac
Δ = 02-4·3·(-306)
Δ = 3672
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:

$\sqrt{\Delta}=\sqrt{3672}=\sqrt{36*102}=\sqrt{36}*\sqrt{102}=6\sqrt{102}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{102}}{2*3}=\frac{0-6\sqrt{102}}{6}
=-\frac{6\sqrt{102}}{6}
=-\sqrt{102}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{102}}{2*3}=\frac{0+6\sqrt{102}}{6}
=\frac{6\sqrt{102}}{6}
=\sqrt{102}
$