X2+2x=52

Solution for X2+2x=52 equation:

X2+2X=52

We move all terms to the left:

X2+2X-(52)=0

We add all the numbers together, and all the variables

X^2+2X-52=0

a = 1; b = 2; c = -52;
Δ = b2-4ac
Δ = 22-4·1·(-52)
Δ = 212
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:

$\sqrt{\Delta}=\sqrt{212}=\sqrt{4*53}=\sqrt{4}*\sqrt{53}=2\sqrt{53}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{53}}{2*1}=\frac{-2-2\sqrt{53}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{53}}{2*1}=\frac{-2+2\sqrt{53}}{2}
$