(x+2)(x-2)+5=5(x+1)

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Solution for (x+2)(x-2)+5=5(x+1) equation: 



(x+2)(x-2)+5=5(x+1)

We move all terms to the left:

(x+2)(x-2)+5-(5(x+1))=0

We use the square of the difference formula

x^2-(5(x+1))-4+5=0



We calculate terms in parentheses: -(5(x+1)), so:

5(x+1)

We multiply parentheses

5x+5

Back to the equation:

-(5x+5)



We add all the numbers together, and all the variables

x^2-(5x+5)+1=0

We get rid of parentheses

x^2-5x-5+1=0

We add all the numbers together, and all the variables

x^2-5x-4=0

a = 1; b = -5; c = -4;
Δ = b2-4ac
Δ = -52-4·1·(-4)
Δ = 41
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{-(-5)-\sqrt{41}}{2*1}=\frac{5-\sqrt{41}}{2}
$


$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{41}}{2*1}=\frac{5+\sqrt{41}}{2}
$

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