X2+48x-432=0

Solution for X2+48x-432=0 equation:

X2+48X-432=0

We add all the numbers together, and all the variables

X^2+48X-432=0

a = 1; b = 48; c = -432;
Δ = b2-4ac
Δ = 482-4·1·(-432)
Δ = 4032
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:

$\sqrt{\Delta}=\sqrt{4032}=\sqrt{576*7}=\sqrt{576}*\sqrt{7}=24\sqrt{7}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-24\sqrt{7}}{2*1}=\frac{-48-24\sqrt{7}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+24\sqrt{7}}{2*1}=\frac{-48+24\sqrt{7}}{2}
$