X(x+5)=x+77

Solution for X(x+5)=x+77 equation:

X(X+5)=X+77

We move all terms to the left:

X(X+5)-(X+77)=0

We multiply parentheses

X^2+5X-(X+77)=0

We get rid of parentheses

X^2+5X-X-77=0

We add all the numbers together, and all the variables

X^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
$