24-6x=x2

Solution for 24-6x=x2 equation:

24-6x=x2

We move all terms to the left:

24-6x-(x2)=0

We add all the numbers together, and all the variables

-1x^2-6x+24=0

a = -1; b = -6; c = +24;
Δ = b2-4ac
Δ = -62-4·(-1)·24
Δ = 132
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:

$\sqrt{\Delta}=\sqrt{132}=\sqrt{4*33}=\sqrt{4}*\sqrt{33}=2\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{33}}{2*-1}=\frac{6-2\sqrt{33}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{33}}{2*-1}=\frac{6+2\sqrt{33}}{-2}
$