2x^2-14x+49=x^2+2x=1

Solution for 2x^2-14x+49=x^2+2x=1 equation:

2x^2-14x+49=x^2+2x=1

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

x^2-16x+49=0

a = 1; b = -16; c = +49;
Δ = b2-4ac
Δ = -162-4·1·49
Δ = 60
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{60}=\sqrt{4*15}=\sqrt{4}*\sqrt{15}=2\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-2\sqrt{15}}{2*1}=\frac{16-2\sqrt{15}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+2\sqrt{15}}{2*1}=\frac{16+2\sqrt{15}}{2}
$