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

Solution for x^2-14x+49=x+2 equation:

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

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

x^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}
$