21-7w=w(3-w)

Solution for 21-7w=w(3-w) equation:

21-7w=w(3-w)

We move all terms to the left:

21-7w-(w(3-w))=0

We add all the numbers together, and all the variables

-7w-(w(-1w+3))+21=0


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

w(-1w+3)

We multiply parentheses

-1w^2+3w

Back to the equation:

-(-1w^2+3w)


We get rid of parentheses

1w^2-3w-7w+21=0

We add all the numbers together, and all the variables

w^2-10w+21=0

a = 1; b = -10; c = +21;
Δ = b2-4ac
Δ = -102-4·1·21
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-4}{2*1}=\frac{6}{2}
=3
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+4}{2*1}=\frac{14}{2}
=7
$