4w^2+2w=^2-8w^2

Solution for 4w^2+2w=^2-8w^2 equation:

4w^2+2w=^2-8w^2

We move all terms to the left:

4w^2+2w-(^2-8w^2)=0

We get rid of parentheses

4w^2+8w^2+2w-^2=0

We add all the numbers together, and all the variables

12w^2+2w=0

a = 12; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·12·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2}{2*12}=\frac{-4}{24}
=-1/6
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2}{2*12}=\frac{0}{24}
=0
$