x^2-24x=144=49

Solution for x^2-24x=144=49 equation:

x^2-24x=144=49

We move all terms to the left:

x^2-24x-(144)=0

a = 1; b = -24; c = -144;
Δ = b2-4ac
Δ = -242-4·1·(-144)
Δ = 1152
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:

$\sqrt{\Delta}=\sqrt{1152}=\sqrt{576*2}=\sqrt{576}*\sqrt{2}=24\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-24\sqrt{2}}{2*1}=\frac{24-24\sqrt{2}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+24\sqrt{2}}{2*1}=\frac{24+24\sqrt{2}}{2}
$