X2+48x-144=0

Solution for X2+48x-144=0 equation:

X2+48X-144=0

We add all the numbers together, and all the variables

X^2+48X-144=0

a = 1; b = 48; c = -144;
Δ = b2-4ac
Δ = 482-4·1·(-144)
Δ = 2880
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:

$\sqrt{\Delta}=\sqrt{2880}=\sqrt{576*5}=\sqrt{576}*\sqrt{5}=24\sqrt{5}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-24\sqrt{5}}{2*1}=\frac{-48-24\sqrt{5}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+24\sqrt{5}}{2*1}=\frac{-48+24\sqrt{5}}{2}
$