810=2w^2/3

Solution for 810=2w^2/3 equation:

810=2w^2/3

We move all terms to the left:

810-(2w^2/3)=0

We get rid of parentheses

-2w^2/3+810=0

We multiply all the terms by the denominator


-2w^2+810*3=0

We add all the numbers together, and all the variables

-2w^2+2430=0

a = -2; b = 0; c = +2430;
Δ = b2-4ac
Δ = 02-4·(-2)·2430
Δ = 19440
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:

$\sqrt{\Delta}=\sqrt{19440}=\sqrt{1296*15}=\sqrt{1296}*\sqrt{15}=36\sqrt{15}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-36\sqrt{15}}{2*-2}=\frac{0-36\sqrt{15}}{-4}
=-\frac{36\sqrt{15}}{-4}
=-\frac{9\sqrt{15}}{-1}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+36\sqrt{15}}{2*-2}=\frac{0+36\sqrt{15}}{-4}
=\frac{36\sqrt{15}}{-4}
=\frac{9\sqrt{15}}{-1}
$