77=w(w+4)

Solution for 77=w(w+4) equation:

77=w(w+4)

We move all terms to the left:

77-(w(w+4))=0


We calculate terms in parentheses: -(w(w+4)), so:

w(w+4)

We multiply parentheses

w^2+4w

Back to the equation:

-(w^2+4w)


We get rid of parentheses

-w^2-4w+77=0

We add all the numbers together, and all the variables

-1w^2-4w+77=0

a = -1; b = -4; c = +77;
Δ = b2-4ac
Δ = -42-4·(-1)·77
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-18}{2*-1}=\frac{-14}{-2}
=+7
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+18}{2*-1}=\frac{22}{-2}
=-11
$