(x+1)(x+9)=3

Solution for (x+1)(x+9)=3 equation:

(x+1)(x+9)=3

We move all terms to the left:

(x+1)(x+9)-(3)=0

We multiply parentheses ..

(+x^2+9x+x+9)-3=0

We get rid of parentheses

x^2+9x+x+9-3=0

We add all the numbers together, and all the variables

x^2+10x+6=0

a = 1; b = 10; c = +6;
Δ = b2-4ac
Δ = 102-4·1·6
Δ = 76
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:

$\sqrt{\Delta}=\sqrt{76}=\sqrt{4*19}=\sqrt{4}*\sqrt{19}=2\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{19}}{2*1}=\frac{-10-2\sqrt{19}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{19}}{2*1}=\frac{-10+2\sqrt{19}}{2}
$