51=x^2+2x

Solution for 51=x^2+2x equation:

51=x^2+2x

We move all terms to the left:

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

We get rid of parentheses

-x^2-2x+51=0

We add all the numbers together, and all the variables

-1x^2-2x+51=0

a = -1; b = -2; c = +51;
Δ = b2-4ac
Δ = -22-4·(-1)·51
Δ = 208
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:

$\sqrt{\Delta}=\sqrt{208}=\sqrt{16*13}=\sqrt{16}*\sqrt{13}=4\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-4\sqrt{13}}{2*-1}=\frac{2-4\sqrt{13}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+4\sqrt{13}}{2*-1}=\frac{2+4\sqrt{13}}{-2}
$