24x-8=x2

Solution for 24x-8=x2 equation:

24x-8=x2

We move all terms to the left:

24x-8-(x2)=0

We add all the numbers together, and all the variables

-1x^2+24x-8=0

a = -1; b = 24; c = -8;
Δ = b2-4ac
Δ = 242-4·(-1)·(-8)
Δ = 544
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:

$\sqrt{\Delta}=\sqrt{544}=\sqrt{16*34}=\sqrt{16}*\sqrt{34}=4\sqrt{34}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-4\sqrt{34}}{2*-1}=\frac{-24-4\sqrt{34}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+4\sqrt{34}}{2*-1}=\frac{-24+4\sqrt{34}}{-2}
$