x2-48x-4=0

Solution for x2-48x-4=0 equation:

X2-48X-4=0

We add all the numbers together, and all the variables

X^2-48X-4=0

a = 1; b = -48; c = -4;
Δ = b2-4ac
Δ = -482-4·1·(-4)
Δ = 2320
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:

$\sqrt{\Delta}=\sqrt{2320}=\sqrt{16*145}=\sqrt{16}*\sqrt{145}=4\sqrt{145}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-4\sqrt{145}}{2*1}=\frac{48-4\sqrt{145}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+4\sqrt{145}}{2*1}=\frac{48+4\sqrt{145}}{2}
$