7w(2+w)=2(3w-1)

Solution for 7w(2+w)=2(3w-1) equation:

7w(2+w)=2(3w-1)

We move all terms to the left:

7w(2+w)-(2(3w-1))=0

We add all the numbers together, and all the variables

7w(w+2)-(2(3w-1))=0

We multiply parentheses

7w^2+14w-(2(3w-1))=0


We calculate terms in parentheses: -(2(3w-1)), so:

2(3w-1)

We multiply parentheses

6w-2

Back to the equation:

-(6w-2)


We get rid of parentheses

7w^2+14w-6w+2=0

We add all the numbers together, and all the variables

7w^2+8w+2=0

a = 7; b = 8; c = +2;
Δ = b2-4ac
Δ = 82-4·7·2
Δ = 8
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:

$\sqrt{\Delta}=\sqrt{8}=\sqrt{4*2}=\sqrt{4}*\sqrt{2}=2\sqrt{2}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{2}}{2*7}=\frac{-8-2\sqrt{2}}{14}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{2}}{2*7}=\frac{-8+2\sqrt{2}}{14}
$