5x^2-48x-4=0

Solution for 5x^2-48x-4=0 equation:

5x^2-48x-4=0

a = 5; b = -48; c = -4;
Δ = b2-4ac
Δ = -482-4·5·(-4)
Δ = 2384
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:

$\sqrt{\Delta}=\sqrt{2384}=\sqrt{16*149}=\sqrt{16}*\sqrt{149}=4\sqrt{149}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-4\sqrt{149}}{2*5}=\frac{48-4\sqrt{149}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+4\sqrt{149}}{2*5}=\frac{48+4\sqrt{149}}{10}
$