7-x=x^2-2x+7

Solution for 7-x=x^2-2x+7 equation:

7-x=x^2-2x+7

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-1x^2+x=0

a = -1; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·(-1)·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-1}{2*-1}=\frac{-2}{-2}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*-1}=\frac{0}{-2}
=0
$