4x+77=x*x

Solution for 4x+77=x*x equation:

4x+77=x*x

We move all terms to the left:

4x+77-(x*x)=0

We add all the numbers together, and all the variables

4x-(+x*x)+77=0

We get rid of parentheses

4x-x*x+77=0

Wy multiply elements

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