77=4x+x^2

Solution for 77=4x+x^2 equation:

77=4x+x^2

We move all terms to the left:

77-(4x+x^2)=0

We get rid of parentheses

-x^2-4x+77=0

We add all the numbers together, and all the variables

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

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