w^2=2w^2+21w+14

Solution for w^2=2w^2+21w+14 equation:

w^2=2w^2+21w+14

We move all terms to the left:

w^2-(2w^2+21w+14)=0

We get rid of parentheses

w^2-2w^2-21w-14=0

We add all the numbers together, and all the variables

-1w^2-21w-14=0

a = -1; b = -21; c = -14;
Δ = b2-4ac
Δ = -212-4·(-1)·(-14)
Δ = 385
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-\sqrt{385}}{2*-1}=\frac{21-\sqrt{385}}{-2}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+\sqrt{385}}{2*-1}=\frac{21+\sqrt{385}}{-2}
$