x-3=x^2-10x+25

Solution for x-3=x^2-10x+25 equation:

x-3=x^2-10x+25

We move all terms to the left:

x-3-(x^2-10x+25)=0

We get rid of parentheses

-x^2+x+10x-25-3=0

We add all the numbers together, and all the variables

-1x^2+11x-28=0

a = -1; b = 11; c = -28;
Δ = b2-4ac
Δ = 112-4·(-1)·(-28)
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{-(11)-3}{2*-1}=\frac{-14}{-2}
=+7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+3}{2*-1}=\frac{-8}{-2}
=+4
$