x+6=(x+4)(x+4)

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

x+6=(x+4)(x+4)

We move all terms to the left:

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

We multiply parentheses ..

-((+x^2+4x+4x+16))+x+6=0


We calculate terms in parentheses: -((+x^2+4x+4x+16)), so:

(+x^2+4x+4x+16)

We get rid of parentheses

x^2+4x+4x+16

We add all the numbers together, and all the variables

x^2+8x+16

Back to the equation:

-(x^2+8x+16)


We add all the numbers together, and all the variables

x-(x^2+8x+16)+6=0

We get rid of parentheses

-x^2+x-8x-16+6=0

We add all the numbers together, and all the variables

-1x^2-7x-10=0

a = -1; b = -7; c = -10;
Δ = b2-4ac
Δ = -72-4·(-1)·(-10)
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-3}{2*-1}=\frac{4}{-2}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+3}{2*-1}=\frac{10}{-2}
=-5
$