w^2-6=15-9w^2

Solution for w^2-6=15-9w^2 equation:

w^2-6=15-9w^2

We move all terms to the left:

w^2-6-(15-9w^2)=0

We get rid of parentheses

w^2+9w^2-15-6=0

We add all the numbers together, and all the variables

10w^2-21=0

a = 10; b = 0; c = -21;
Δ = b2-4ac
Δ = 02-4·10·(-21)
Δ = 840
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:

$\sqrt{\Delta}=\sqrt{840}=\sqrt{4*210}=\sqrt{4}*\sqrt{210}=2\sqrt{210}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{210}}{2*10}=\frac{0-2\sqrt{210}}{20}
=-\frac{2\sqrt{210}}{20}
=-\frac{\sqrt{210}}{10}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{210}}{2*10}=\frac{0+2\sqrt{210}}{20}
=\frac{2\sqrt{210}}{20}
=\frac{\sqrt{210}}{10}
$