(x+2)(x-2)=(x+1)2+7

Solution for (x+2)(x-2)=(x+1)2+7 equation:

(x+2)(x-2)=(x+1)2+7

We move all terms to the left:

(x+2)(x-2)-((x+1)2+7)=0

We use the square of the difference formula

x^2-((x+1)2+7)-4=0


We calculate terms in parentheses: -((x+1)2+7), so:

(x+1)2+7

We multiply parentheses

2x+2+7

We add all the numbers together, and all the variables

2x+9

Back to the equation:

-(2x+9)


We get rid of parentheses

x^2-2x-9-4=0

We add all the numbers together, and all the variables

x^2-2x-13=0

a = 1; b = -2; c = -13;
Δ = b2-4ac
Δ = -22-4·1·(-13)
Δ = 56
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:

$\sqrt{\Delta}=\sqrt{56}=\sqrt{4*14}=\sqrt{4}*\sqrt{14}=2\sqrt{14}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{14}}{2*1}=\frac{2-2\sqrt{14}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{14}}{2*1}=\frac{2+2\sqrt{14}}{2}
$