77=l(l-4)

Solution for 77=l(l-4) equation:

77=l(l-4)

We move all terms to the left:

77-(l(l-4))=0


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

l(l-4)

We multiply parentheses

l^2-4l

Back to the equation:

-(l^2-4l)


We get rid of parentheses

-l^2+4l+77=0

We add all the numbers together, and all the variables

-1l^2+4l+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:
$l_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$l_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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