2w(5w+2)=5w+2

Solution for 2w(5w+2)=5w+2 equation:

2w(5w+2)=5w+2

We move all terms to the left:

2w(5w+2)-(5w+2)=0

We multiply parentheses

10w^2+4w-(5w+2)=0

We get rid of parentheses

10w^2+4w-5w-2=0

We add all the numbers together, and all the variables

10w^2-1w-2=0

a = 10; b = -1; c = -2;
Δ = b2-4ac
Δ = -12-4·10·(-2)
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-9}{2*10}=\frac{-8}{20}
=-2/5
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+9}{2*10}=\frac{10}{20}
=1/2
$