(x+3)(x+7)=11

Solution for (x+3)(x+7)=11 equation:

(x+3)(x+7)=11

We move all terms to the left:

(x+3)(x+7)-(11)=0

We multiply parentheses ..

(+x^2+7x+3x+21)-11=0

We get rid of parentheses

x^2+7x+3x+21-11=0

We add all the numbers together, and all the variables

x^2+10x+10=0

a = 1; b = 10; c = +10;
Δ = b2-4ac
Δ = 102-4·1·10
Δ = 60
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{60}=\sqrt{4*15}=\sqrt{4}*\sqrt{15}=2\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{15}}{2*1}=\frac{-10-2\sqrt{15}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{15}}{2*1}=\frac{-10+2\sqrt{15}}{2}
$