3w^2-5=13

Solution for 3w^2-5=13 equation:

3w^2-5=13

We move all terms to the left:

3w^2-5-(13)=0

We add all the numbers together, and all the variables

3w^2-18=0

a = 3; b = 0; c = -18;
Δ = b2-4ac
Δ = 02-4·3·(-18)
Δ = 216
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:

$\sqrt{\Delta}=\sqrt{216}=\sqrt{36*6}=\sqrt{36}*\sqrt{6}=6\sqrt{6}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{6}}{2*3}=\frac{0-6\sqrt{6}}{6}
=-\frac{6\sqrt{6}}{6}
=-\sqrt{6}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{6}}{2*3}=\frac{0+6\sqrt{6}}{6}
=\frac{6\sqrt{6}}{6}
=\sqrt{6}
$