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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-1x^2+15x-47=0

a = -1; b = 15; c = -47;
Δ = b2-4ac
Δ = 152-4·(-1)·(-47)
Δ = 37
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{-(15)-\sqrt{37}}{2*-1}=\frac{-15-\sqrt{37}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+\sqrt{37}}{2*-1}=\frac{-15+\sqrt{37}}{-2}
$