(x+2)(x+1)=(x+15)2+9

Solution for (x+2)(x+1)=(x+15)2+9 equation:

(x+2)(x+1)=(x+15)2+9

We move all terms to the left:

(x+2)(x+1)-((x+15)2+9)=0

We multiply parentheses ..

(+x^2+x+2x+2)-((x+15)2+9)=0


We calculate terms in parentheses: -((x+15)2+9), so:

(x+15)2+9

We multiply parentheses

2x+30+9

We add all the numbers together, and all the variables

2x+39

Back to the equation:

-(2x+39)


We get rid of parentheses

x^2+x+2x-2x+2-39=0

We add all the numbers together, and all the variables

x^2+x-37=0

a = 1; b = 1; c = -37;
Δ = b2-4ac
Δ = 12-4·1·(-37)
Δ = 149
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{149}}{2*1}=\frac{-1-\sqrt{149}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{149}}{2*1}=\frac{-1+\sqrt{149}}{2}
$