30-2x=x2

Solution for 30-2x=x2 equation:

30-2x=x2

We move all terms to the left:

30-2x-(x2)=0

We add all the numbers together, and all the variables

-1x^2-2x+30=0

a = -1; b = -2; c = +30;
Δ = b2-4ac
Δ = -22-4·(-1)·30
Δ = 124
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:

$\sqrt{\Delta}=\sqrt{124}=\sqrt{4*31}=\sqrt{4}*\sqrt{31}=2\sqrt{31}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{31}}{2*-1}=\frac{2-2\sqrt{31}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{31}}{2*-1}=\frac{2+2\sqrt{31}}{-2}
$