x^2-2x=27

Solution for x^2-2x=27 equation:

x^2-2x=27

We move all terms to the left:

x^2-2x-(27)=0

a = 1; b = -2; c = -27;
Δ = b2-4ac
Δ = -22-4·1·(-27)
Δ = 112
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:

$\sqrt{\Delta}=\sqrt{112}=\sqrt{16*7}=\sqrt{16}*\sqrt{7}=4\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-4\sqrt{7}}{2*1}=\frac{2-4\sqrt{7}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+4\sqrt{7}}{2*1}=\frac{2+4\sqrt{7}}{2}
$