(x+7)(x+3)=77

Solution for (x+7)(x+3)=77 equation:

(x+7)(x+3)=77

We move all terms to the left:

(x+7)(x+3)-(77)=0

We multiply parentheses ..

(+x^2+3x+7x+21)-77=0

We get rid of parentheses

x^2+3x+7x+21-77=0

We add all the numbers together, and all the variables

x^2+10x-56=0

a = 1; b = 10; c = -56;
Δ = b2-4ac
Δ = 102-4·1·(-56)
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{-(10)-18}{2*1}=\frac{-28}{2}
=-14
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+18}{2*1}=\frac{8}{2}
=4
$