x+13=(x+7)(x+7)

Solution for x+13=(x+7)(x+7) equation:

x+13=(x+7)(x+7)

We move all terms to the left:

x+13-((x+7)(x+7))=0

We multiply parentheses ..

-((+x^2+7x+7x+49))+x+13=0


We calculate terms in parentheses: -((+x^2+7x+7x+49)), so:

(+x^2+7x+7x+49)

We get rid of parentheses

x^2+7x+7x+49

We add all the numbers together, and all the variables

x^2+14x+49

Back to the equation:

-(x^2+14x+49)


We add all the numbers together, and all the variables

x-(x^2+14x+49)+13=0

We get rid of parentheses

-x^2+x-14x-49+13=0

We add all the numbers together, and all the variables

-1x^2-13x-36=0

a = -1; b = -13; c = -36;
Δ = b2-4ac
Δ = -132-4·(-1)·(-36)
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-5}{2*-1}=\frac{8}{-2}
=-4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+5}{2*-1}=\frac{18}{-2}
=-9
$