Solve w(n-5)=7n-n^2

Evaluate

w (n - 5) = 7 n - n^{2}

Move the expression to the left side

w (n - 5) - (7 n - n^{2}) = 0

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

w (n - 5) - 7 n + n^{2} = 0

Calculate

More Steps

w n - 5 w - 7 n + n^{2} = 0

Collect like terms by calculating the sum or difference of their coefficients

(w - 7) n - 5 w + n^{2} = 0

Rewrite in standard form

n^{2} + (w - 7) n - 5 w = 0

Substitute a= 1,b= w - 7 and c= - 5 w into the quadratic formula n = \frac{- b \pm b ^{2} - 4 a c}{2 a}

n = \frac{- w + 7 \pm ( w - 7 ) ^{2} - 4 ( - 5 w )}{2}

Simplify the expression

More Steps

n = \frac{- w + 7 \pm w ^{2} + 6 w + 49}{2}

Solution

n = \frac{- w + 7 + w ^{2} + 6 w + 49}{2} n = \frac{- w + 7 - w ^{2} + 6 w + 49}{2}

Solve the equation