X(2)-24x-5=0

Solution for X(2)-24x-5=0 equation:

X(2)-24X-5=0

We add all the numbers together, and all the variables

X^2-24X-5=0

a = 1; b = -24; c = -5;
Δ = b2-4ac
Δ = -242-4·1·(-5)
Δ = 596
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:

$\sqrt{\Delta}=\sqrt{596}=\sqrt{4*149}=\sqrt{4}*\sqrt{149}=2\sqrt{149}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-2\sqrt{149}}{2*1}=\frac{24-2\sqrt{149}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+2\sqrt{149}}{2*1}=\frac{24+2\sqrt{149}}{2}
$