(x+1)(x+6)=(x+4)2

Solution for (x+1)(x+6)=(x+4)2 equation:

(x+1)(x+6)=(x+4)2

We move all terms to the left:

(x+1)(x+6)-((x+4)2)=0

We multiply parentheses ..

(+x^2+6x+x+6)-((x+4)2)=0


We calculate terms in parentheses: -((x+4)2), so:

(x+4)2

We multiply parentheses

2x+8

Back to the equation:

-(2x+8)


We get rid of parentheses

x^2+6x+x-2x+6-8=0

We add all the numbers together, and all the variables

x^2+5x-2=0

a = 1; b = 5; c = -2;
Δ = b2-4ac
Δ = 52-4·1·(-2)
Δ = 33
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{33}}{2*1}=\frac{-5-\sqrt{33}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{33}}{2*1}=\frac{-5+\sqrt{33}}{2}
$